On Sunday Saints overcame Swansea 2-0 to secure a third successive league win, collecting a fifth clean sheet of the term in the process.
This season's performances have impressed, and surprised, many, but midfielder Schneiderlin does not think they have yet reached their peak.
"It was very important for us to win that game, because now we have two weeks off and we go to Man United next full of confidence," the Frenchman said.
"It was a very hard game. Swansea is a very good team, they keep very good possession, so we had to dig in sometimes.
"Sometimes we were a bit lucky to not concede a goal, but Artur Boruc made some great saves, and we were lucky with the post as well.
"But I think we showed great character and we showed togetherness to get away with a win.
"I don't think we've reached our best yet, individually or collectively.
"We are a step forward again and got even better, but it's very important for everyone to not get carried away, the fans, the players.
"We have to make sure we are still working very hard, because it's just seven games of the season and we need to play each game as if it was the last and then see how we are at the last game.
Source: PA
Source: PA