Having earned promotion from the Championship last term, the Saints initially struggled for form in the top flight before finishing in relative comfort in 14th place.
Schneiderlin, who swept the board at the club's end-of-season awards ceremony, is now looking for Southampton to push on next term after chairman Nicola Cortese committed himself to the cause.
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"I think that, especially with the people we've played in the second half of the season, we have shown that we deserve to be here for a long time.
"This week we showed that everyone is pulling in the same direction. That is very important for a football club, it's a very hard thing to find."
The 23-year-old featured in all but two of Southampton's league outings this term, scoring five goals along the way, and admits he is now looking forward to a break before pre-season kicks into gear.
"For the first two weeks I am going to switch off completely and think about something else, although I'm probably going to watch the Champions League final!" he continued.
"After that, I am going to switch off from football, but I'll prepare at home by doing the necessary things, so that I can come back in pre-season and be focused right away on having a long campaign and doing the best I can."