United had top scorer Romelu Lukaku carried off on a stretcher early in the game and looked stricken of any thrust or creativity in attack, ending the month with four wins from nine matches in all competitions and without a victory in their last four.
Jose Mourinho’s side began brightly and Lukaku came close to giving them the lead in the third minute when he headed a Juan Mata cross over the bar while Jesse Lingard also narrowly missed the target before the interval with a flicked header.
Paul Pogba had a late strike ruled out as he knocked Nemanja Matic’s rolling shot in from an offside position when the ball looked destined to hit the post.
United began December with a 100 percent record in the league and Europe at Old Trafford but have now failed to win three of their last four home games.
The run of results has left them third in the league with 44 points, 14 behind leaders Manchester City and one behind champions Chelsea, who moved up to second.
Mourinho insisted his side had deserved to win the game and criticised referee Craig Pawson for not giving a penalty in the first half when the ball struck the hand of Maya Yoshida in the area.
“I think we played enough to win, with all the difficulties. We started the game and we lost the striker (Lukaku) and we lost one of only two changes I have on the bench in attacking areas,” Mourinho told a news conference.
“Then a very good referee, one of the most promising young referees in England and Europe too, had a very bad decision that punished us and then the game was about us missing some important chances.”
Southampton came to Old Trafford having been hammered 5-2 by Tottenham Hotspur on Boxing Day and after selling defender Virgil van Dijk to Liverpool but they were rarely in danger of going behind.
They ended a run of 11 league games without recording a clean sheet and move up to 13th in the standings on 20 points.
They were not far from snatching a first win in eight games when Shane Long saw his shot turned over the crossbar by the toe of David de Gea in the second half, while before the interval De Gea dived low to repel a shot from James Ward-Prowse.
“It was a really important point for us, especially after a really sobering few games,” said Southampton captain Yoshida.
“The reaction from the players was great, we’re really happy with that. We showed good spirit today, and now we move onto the next game.”
Meanwhile, Manchester United striker Zlatan Ibrahimovic will be sidelined for a month with a knee injury, manager Jose Mourinho said.
The former Sweden international was not in Saturday’s squad as Mourinho’s men were held to a 0-0 stalemate by Southampton at Old Trafford -- United’s third successive draw.
Ibrahimovic was re-signed by United in the summer, having departed the club at the end of last season, and overcame meniscus and cruciate ligament damage to return to action in late November.
However, Mourinho, who saw Romelu Lukaku carried off on a stretcher during Saturday’s Premier League encounter against Southampton, said Ibrahimovic is set for another injury layoff.
“We lost Ibrahimovic for a month, he stops his run to recovery, he has been running for many months, what he needs is to play,” Mourinho said.