The 23-year-old Frenchman has impressed for the Saints as they battled to stay in the Barclays Premier League and has been linked with a big-money summer move to Arsenal.
"I am happy because I have improved in every way, but I know that I still have steps to progress," he said in an interview with the official Southampton matchday programme.
"This year I have had a good season, but next year I want to be even better. For me, next year is going to be the real thing.
"I want to prove myself to everyone again, and to get even better.
"In football, if you stop improving then you'll automatically go backwards."
Despite all the attention, the young Frenchman intends to keep grounded.
Schneiderlin added: "I am not going to lie and say that I am not happy that people are speaking about me and my games, but there is no point in me having a good season and then disappearing the year after.
"The main thing for me is to keep this going and to be able to be better in every game I play.
"I don't like to judge myself - that is down to other people - but I know that I have the capacity to play in the Premier League and I want to spend the rest of my life playing here."
Source: PA
Source: PA