The Czech Republic outfit took a 3-1 advantage from the first leg in Italy into the contest which left the Serie A club needing to score at least three goals to have any chance of progressing from the qualifiers.
However, Udinese couldn't pull off the miracle and were knocked out of the competition after a draw in Liberec.
Read how the action unfolded in our live commentary below.
5.41pmThe Czech outfit are just 90 minutes from making it to the group stages of the Europa League after a shock 3-1 win in Italy last week. Goals from Serhiy Rybalka, Dzon Delarge and Ondrej Kusnir have put Liberec in complete control of the tie despite a strike from Gabriel Silva.
5.42pmSo that means that Udinese have to score at least three goals if they are going to qualify. Even a 2-0 win for the Italians wouldn't be enough due to the away goals rule. Tough ask, but when you have a striker like Antonio Di Natale in your side, goals are almost a certainty.
2 minLiberec and wearing their white home strip with blue trim and are playing from right to left in this first half.
3 minUdinese are sporting and black and grey striped shirt with black shorts and socks.
4 minIt's been a quiet start to the game on the pitch but the noise from the stands is impressive. Great vocal support for the home team from this Czech crowd.
6 minThere is a short break in play after a clash of heads in the centre circle. Basta is currently off the field receiving some treatment but will be fine to continue once he has been patched up.
7 minPlay is back underway as Udinese regain possession.
9 minIt's been a really slow start to this match. Udinese have had the lion's share of the ball, but haven't yet managed to create a chance. They're biding their time at the moment.
12 minChance for Udinese now as Di Natale prepares to take a corner from the left.
13 minNot a bad delivery as Di Natale curls it all the way towards the far post where Danilo is lurking, but the defender can't quite stretch enough and get his head on the cross.
16 minSAVE! Liberec very nearly put the tie to bed as a costly defensive mistake allows Delarge to thread in Rabusic on the left. The forward bares down on goal and draws out Kelava before trying to sweep the ball with the outside of his boot into the bottom corner, but the keeper is equal to the effort and makes a vital save with his legs.
20 minDespite that Liverec opportunity, Udinese have still dominated this match but are yet to create a proper scoring chance. They need to make the most of the free kicks they are being awarded. Di Natale just floated a cross into the box that was far too easy for Liberec to deal with.
22 minLiberec again have a decent chance as Rabusic plays it to Sural on the right side of the box. His shot looks good but is blocked and heads out of play.
24 minAnd that could be this tie done and dusted as Liberec take the lead thanks to some terrible defending from Udinese. The hosts have a throw out on the right which is rocketed into the box and is allowed to bounce twice without anyone touching it before Delarge wriggles free from his marker to smash the ball into the back of the net from an acute angle. Great finish but shocking defending.
25 minSo that makes it 4-1 on aggregate to Liberec now which leaves Udinese needing to score three goals to take the tie to extra time, as things stand.
28 minAt the moment, it looks more likely that Liverec will score a second rather than for Udinese to get off the mark. The Italians just haven't been clinical enough so far.
29 minLiberec loft another long throw into the box, but this time Udinese can deal with it thanks to Heurtaux's headed clearance.
31 minUDINESE CHANGE The Italians have been forced into an early change as Maicosuel comes on in place of the injured Domizzi.
34 minUdinese have the ball in the back of the net but Muriel is flagged early for being offside before he can volley across for Di Natale to convert.
36 minFollowing that change, Udinese appear to be lining up with a 4-3-1-2 formation.
39 minThe games become a bit scrappy in the last few minutes with tackles flying in everywhere. Liberec still look comfortable at the moment though.
6.48pmSo Liberec are just 45 minutes away from securing their place in the Europa League although it looks pretty certain that they will be there anyway. Udinese need to score at least twice in the second half, but they haven't been clinical enough in this match so far.
6.49pmDelarge put Liberec in front midway through the first half before Lazzari levelled things up just before the break.
6.59pmLiberec have made their way back onto the field to a big ovation from the crowd.
7pmUdinese are back out as well, and they will have kick off.
46 minKICK OFF! Udinese get the second half underway.
47 minCHANCE! Early opportunity for Udinese in this half as Muriel holds off his marker on the left before lashing a shot at goal from just outside the area. However, his effort goes just wide of the near post.
49 minA very stop-start beginning to this second half due to fouls. Liberec seem keen on going back in front just to see off the tie for good, Udinese are breaking well at the moment though.
53 minNot a lot to update you on at the moment. We've not really seen any chances, just a lot of fouls and rolling around on the floor, in particular from the home team.
58 minLiberec are on top at the moment and are enjoying most of the possession. They're taking their time over throwings and set-pieces as well as they look to wind down the clock.
61 minLiberec work the ball from the right touchline into the centre where Pavelka is lurking. He takes a touch and then fancies a pop at goal from 30 yards out. He smashes the ball low with his left foot, but it's not enough to trouble Kelava, who makes a simple stop.
63 minCHANCE! That's the closest we've come to a goal in this second half and it was courtesy of Liberec. A free kick is floated into the penalty area from the midway point of the Udinese half on the right. The ball dips towards the penalty spot where Fleisman meets the ball with his head, but flicks it just over the bar.
67 minYELLOW CARD Fleisman goes into the referee's notebook for unsporting behaviour, also known as time wasting.
70 minStill nothing in the way of chances for Udinese. They've got 20 minutes to pull off a miracle in the Czech Republic so they ought to start having a go at goal soon.
72 minRED CARD! Pereyra is shown a second yellow card for an off the ball incident. He made a heavy challenge on one Liberec player before retaliating to a collision with another.
74 minMission impossible for Udinese now. Need two goals to just force extra time and are down to 10 men.
77 minBoy is this game getting scrappy now. Udinese are trying their best to try to win the all back but cannot help but commit fouls.
80 minUDINESE CHANGE Di Natale has been brought off by manager Francesco Guidolin and replaced by Nicolas Lopez.
82 minLiberec doing their best to wind down the clock and doing it relatively successful. They can taste the group stages.
83 minLIBEREC CHANGE Sural has been taken off with Lubos Kolar brought on.
86 minLIBEREC CHANGE Another alteration to waste time by the hosts. Rabusic is brought off to a standing ovation while Vladislav Kalitvintsev enters the fray.
89 minStill all Liberec, Udinese have all but given up as we await to see how much added time there will be.
90 minLIBEREC CHANGE Lubos Husek has come on for the final few minutes in place of Rybalka.
90 minThere will be three more minutes of this match to go.