United required a victory in the final game of the Premier League campaign and defeat for Tottenham against Aston Villa to steal sixth spot, but results transpired against Ryan Giggs' men.
Tottenham's win over Villa coupled with a share of the spoils at St Mary's Stadium means United miss out on Europe having played in continental competition for the past 23 seasons.
Both sides pushed for a winner and were guilty of missing chances to seal all three points. The draw, combined with Tottenham's win over Villa, sees United finish the campaign in seventh, while Southampton are one position behind them.
Victor Wanyama was first to threaten the United goal with a low strike in the 10th minute and even Adam Lallana's flick in front of the Spanish goalkeeper was not able to find the back of the net.
An elbow from Lambert in the build-up left Nemanja Vidic on the floor, but play was allowed to continue and the burly forward emphatically fired past De Gea from close range after being played in by Steven Davis' neat pass.
United's players surrounded Mike Dean to bemoan the decision, but the goal stood, while Vidic – making his final appearance before joining Serie A giants Inter - received treatment on a bleeding nose.
The visitors, who left Tuesday's hero James Wilson out of their squad, only created their first sight of goal in the 34th minute as Chris Smalling met a loose ball on the edge of the penalty area, but he skewed his low shot wide without testing Boruc.
Giggs' decision to introduce Michael Carrick at half-time had an immediate impact for the visitors as it released Mata into a more creative role.
United's second-half revival continued and just after the hour they should have been ahead through Darren Fletcher.
