The midfielder's 85th-minute strike looked to have given Southampton a warranted win over the Latics, but Shaun Maloney levelled matters soon afterwards.
So, having seen his team dominate proceedings at the DW Stadium, Schneiderlin was left frustrated come full time.
"We could have taken all three points – we came here with the intention to win the game," said the Frenchman.
"I think we did everything we could, but we've conceded two goals from corners.
"From open play, you couldn't really see how they would score so we're disappointed to concede a goal like that in the last minute.
"Since the new manager came, we've played fantastic football for three games and we've been unlucky not to win," he added.
"We couldn't get near Wigan when we played them at home, and today they didn't hurt us at all.
"We were all over them so they couldn't really do anything, and that's because the manager wants us to play a high-pressure game with a lot of movement.
"The manager told us before the game that he wanted to win to put a big gap between them and us because it was a 'six-pointer'.
"But we've kept them three points behind us, and now we're going to try to put a bigger gap between us in the next few games."
Schneiderlin's goal – his third of the season – was the result of a superb break led by Jay Rodriguez, whose low cross was duly converted by the midfielder.
But Morgan revealed there was another player who had a key role in the strike – opening goalscorer Rickie Lambert.
"I wanted to keep my position in midfield but Rickie Lambert was behind me and he was telling me to push so I told him I would!" he said.
"It was a fantastic run from Jay and a good pass, so I just had to push the ball into the back of the net.
"It was a good goal, and I'm happy because I've been trying to work hard on that part of my game and to score more goals."
Saints will now begin preparations for their next game – the visit of reigning Barclays Premier League champions Manchester City a week today.
And, despite them only yielding three points, Schneiderlin says the team's three most-recent performances should give them reason to be cheerful ahead of that match.
"We are very confident that we can push on," he insisted. "In the last three games, we could have taken at least seven points but we've just got two.
"That's disappointing, but we're going to make sure that we keep playing the same way in the next few games because I'm sure we're going to win some soon.
"We want to win every game we play, and we will want to do that again against Manchester City next week."