The 22-year-old midfielder netted his first-ever Premier League goal to give Nigel Adkins' men the lead before Robin van Persie completed a hat-trick to deny the Saints
The Frenchman scored his maiden Premier League goal to give the Saints a 2-1 lead in the 55th minute but Robin van Persie struck twice in the final three minutes to complete his hat-trick and take the three points.
And the 22-year-old revealed his disappointment with the result, admitting that it made his landmark strike a bittersweet moment.
"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," he told the club's official website.
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"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."
Despite his side's late defeat, the former Strasbourg man insisted that Nigel Adkins' side could take plenty of inspiration from their performance.
"Manchester United may have won the game but there are still a lot of positives to take away," Schneiderlin declared.
"In both games against Manchester City and United we went 2-1 up so you could say we lost six points but these are the two best sides in England so we've done very well against them and we need to focus on the next game.
"We have a little break now to adjust everything and hopefully against Arsenal we'll be on top again but this time we'll win it."
The midfielder also dismissed suggestions that the upcoming international break may disrupt Southampton's preparations for their clash with the Gunners.
"I don't think it's a bad thing," he opined. "We have some new players and I know some are going on international duty but we have a week and a half now to prepare for the next game and to work on everything to come back even stronger.
"It's going to be a long season – it's a marathon – and we need to be ready now to win games when we're in front."