The visitors took a shock third minute lead via Jay Rodriguez after a poor back pass from Michael Carrick.
Wayne Rooney put United well in control with a quick-fire brace before the Saints dominated the second half but could not find the equaliser their play deserved.
The defeat leaves the Saints hovering three points above the drop zone and Pochettino told Sky Sports: "I'm very frustrated and angry because I always like to win.
"Having said that we knew that Manchester United are an amazing team with quality players.
"Judging how we played in the second half I think we deserved a bit more than leaving here with nothing."
Opposing boss Alex Ferguson said the Saints were the best team to come to Old Trafford this season but Pochettino would have preferred points on the board.
"His words don't really serve as a consolation to me," added Pochettino.
"But I want to say thank you for those words and it also reinforces the way that we want the team to go forward."