The Dutchman was right to do so as his team are now 22 points adrift of the top spot after losing 1-0 to leaders Leicester City at the King Power Stadium last weekend.
Koeman's side matched the title favourites for 38 minutes before Wes Morgan struck to score the one and only goal of the contest, ensuring that Leicester need to win four more games to take home the English crown.
Grabbing a European spot was always Southampton's ambition at the start of the season, but they are six points behind Manchester United, who currently occupy the Europa League spot in the table.
The Saints have been inconsistent on the pitch of late having recorded two victories, one draw and two defeats in their last five top-flight games.
Prior to the result against Leicester at the weekend, Koeman's side showed some grit and determination to come from 2-0 down to earn a 3-2 victory over Liverpool at St Mary's.
Sadio Mane led the charge as he reduced Liverpool's lead with a goal in the 64th minute, and after Graziano Pelle added an equaliser inside the final 10 minutes of the game, the midfielder grabbed the winner four minutes from time.
Southampton failed to hold on to that momentum against Leicester, but as they prepare to host Newcastle this weekend they head into the match unbeaten at home in their last two games.
The Saints have won exactly half of their 18 league games on home soil.
Recent form: LLDWWL
Rafael Benitez always had a big job on his hands when he replaced Steve McClaren last month, but Newcastle's wannabe saviour has an even tougher task given that he is three games without a win.
The Spaniard's first game in charge was a difficult one as his new team took on the Premier League leaders Leicester City, who went on to claim a 1-0 win over the Magpies on home turf.
The next game was against arch rivals Sunderland and Benitez's men managed to claim a point in the Tyne-Wear derby, but they were dealt a huge blow in their quest for survival when they faced Norwich City at Carrow Road last weekend.
That result has left Newcastle six points from safety with just seven games left to play, and in those games, they will face Southampton, Swansea City, Manchester City, Liverpool, Crystal Palace, Aston Villa and Tottenham Hotspur.
The North-East outfit have only won six of their 31 league games this season, and two of them came away from home, proving that they are big underdogs heading to St Mary's.
Benitez likes his teams to tighten up at the back, but he still has some work to do in that area as they have conceded four goals in their last two matches.
Recent form: LLLLDL
Jay Rodriguez, who has been on the treatment table for the last four months, returned to the bench last Sunday and could be given a cameo role against Newcastle.
Mitrovic could start after scoring against Norwich the last time out, meaning that Papiss Cisse could drop to the bench,
Southampton possible starting lineup:
Forster; Cedric, Fonte, Van Dijk, Bertrand; Clasie, Wanyama, Davis, Mane; Long, Pelle
Newcastle United possible starting lineup:
Darlow; Janmaat, Mbemba, Taylor, Anita; Tiote, Shelvey; Townsend, Sissoko, Wijnaldum; Mitrovic
Head To Head
On the opening day of the season, Newcastle hosted Southampton at St James' Park and were close to claiming a 2-1 victory after Cisse cancelled out Pelle's goal and Georginio Wijnaldum added a second.
However, in the 79th minute, Shane Long managed to seal a point for the Saints after coming off the substitutes' bench.
Excluding the season opener, in the last four matches between these two clubs, Southampton have ran out winners three times; two of those results ended in 4-0 wins in 2014.
Newcastle have managed to earn just a single 1-1 draw in their last five games against the Saints.
The Dugout Podcast
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We say: Southampton 2-0 Newcastle United
Southampton and Newcastle may have played out a 2-2 draw earlier in the season, but a lot has changed for both clubs as they are at completely opposite ends of the table. The Magpies are desperate for a result, but they come up against a Saints team who have quality players to get a result in front of their home fans.