"We did play well but I'm upset at not getting a draw at least. It doesn't console me," he told BBC Sport.
"I think in the second half we played as we should have done for the whole game. I think it's important for the team to know we can play that well."
United boss Alex Ferguson described Southampton as the "best team" to play at Old Trafford this season after the game, remarks which Pochettino admits made him "very proud".
The result leaves United seven points clear at the top of the Premier League.