The midfielder helped the team extend their unbeaten record at St Mary's and secure their third win on the bounce, with a 2-0 home success over Swansea.
"I don't think we've reached our best yet, individually or collectively," Schneiderlin told the Daily Echo.
"It's very important for everyone to not get carried away.
"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 it was 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."
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