A third draw in succession for the Red Devils over the festive period places them 14 points adrift of leaders Manchester City, who have a game in hand still to play, and now one behind Chelsea in second.
United should have snatched a much-needed victory in the final 10 minutes but Nemanja Matic's goalbound effort was pounced on by Paul Pogba in an offside position, meaning that the points were shared.
Prior to being taken off with a facial injury, Romelu Lukaku squandered a glorious chance by heading clean over the crossbar when picked out 10 yards from goal.
In between those two shots, United were dealt that early blow of losing Lukaku following a clash of heads with Wesley Hoedt, likely ruling him out of the New Year's Day return to former club Everton.
Marcus Rashford was summoned from the bench and made a good impact, sparking a quick counter-attack that disappointingly ended with Henrikh Mkhitaryan - handed a first league start in close to two months - miscuing the subsequent cross.
Southampton, winners here on two of their last three visits prior to today, could not make the most of their big chance of the first half as Hoedt failed to find the target with his close-range header.
United should have taken a lead into the break, though, as soon after having a penalty shout rejected through a clear Maya Yoshida handball, a cross came into the box for Jesse Lingard to glance wide unmarked.
Despite being horribly out of form heading into this final match of 2017, Southampton were looking bright early in the second half and were so nearly in front when Shane Long got ahead of Matic.
Mkhitaryan had a weak shot kept out by McCarthy before being replaced by Anthony Martial, and then came a huge moment in the match as Matic helped the ball goalwards for Pogba to prod it over the line from less than a yard out.
The officials rightly ruled that the Frenchman was offside, but the ball appeared to be creeping past McCarthy without the intervention of Pogba.
That would prove to be the final clear-cut chance of the match, meaning that United are stuck on two wins from their last seven matches in all competitions during a month to forget.
Manchester United (4-2-3-1): De Gea; Young, Lindelof, Jones, Shaw; Matic, Pogba; Mata, Lingard, Mkhitaryan (Martial 65'); Lukaku (Rashford 14')
Southampton (4-2-3-1): McCarthy; Stephens, Yoshida, Hoedt, McQueen; Romeu, Hojbjerg; Tadic (Lemina 82'), Ward-Prowse, Boufal (Redmond 85'); Long (Gabbiadini 80')