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.
"Now every team is going to see Southampton fourth in the table and everyone is going to play very hard against us now, so it's up to us to step up and to be even better."
Next up, as Schneiderlin mentions, is the unenviable task of taking points from Manchester United.
David Moyes' side sit in ninth position, four points behind Saints, whose second-half performance in the north west last season was lauded by Sir Alex Ferguson as the best seen at Old Trafford that campaign.
"I'm telling you we are going to work very hard, because after last time against Norwich that's what we did in the last international break," Schneiderlin said.
"We will work very hard to go to Man U full of energy and at our best. It's time mentally to relax a bit, but physically to work.
"It's going to be very intense, but that's what we need, to keep everyone working hard."
It has to be said that Southampton are somewhat fortunate to be heading to Manchester United on such a run.
Swansea dominated for the most part at St Mary's on Sunday, with only last-ditch defending, the goal frame and a string of Boruc saves keeping them at bay.
It was an impressive performance given their European exertions against St Gallen on Thursday evening, but that was of little consolation to the players.
"It was a big disappointment for us," right-back Angel Rangel said.
"We created very good chances and dominated the majority of the game, but the ball just wouldn't go in.
"We should have got something from the game - It was just one of those days.
"We have two weeks rest and hopefully it will recharge the batteries and ensure we are ready for the next few games which are very important for us.
"It will be good to rest as we've had a lot of games in a short space of time, but it will be a long 13 days as we go into the break on the back of a defeat."