Schneiderlin scored his first goal at St Mary's to give his side a 2-1 lead, only to see Robin van Persie complete his hat-trick in stoppage time to secure United all three points.
The French midfielder told the club's official website: "It's my first Premier League goal and my first one at St Mary's as well so that's good but I'm gutted that we lost the game and that's the only thing in my mind right now.
"We gave everything for 87 minutes, and in five minutes we lost the game. That's what we need to learn now to win games because that's the second time we've been 2-1 up and finished 3-2 so all the effort we have put in has been for nothing.
"We've learned a lot from this match though and we're going to try to work hard on the training ground on the bad things that happened because that is important."
Saints visit the Emirates to play Arsenal in their next match, looking to secure their first Premier League points of the season.