Saints fell behind during the first half but controlled the game for large periods as they turned the match on its head during the second half.
Pochettino admitted that, although he was happy with the performance, there was also disappointment that he could not gain his first win in charge.
"There are two different feelings," Pochettino told Saints Player.
"First because we played well, and secondly, because we could and should have won the game, so we are disappointed with the result.
"I am happy with the performance of the team, and although I am disappointed with the result, we played well today, so I am happy with that.
"You can never count on winning. You always have to wait until the end of the match and that is the same in football all of the time, you can't rest on your laurels, you have to play until the end.
"Today I am sad for the players who have played very well and made a great effort, but unfortunately we haven't come away with the result.
"I am also very pleased with the supporters who have given us great support here today."