The Frenchman, who scored twice in Saturday's 3-1 win over West Ham, reportedly handed in a transfer request last month amid interest from former boss Mauricio Pochettino at Tottenham, and later criticised his club on social media.
Saints chairman Ralph Kruger has insisted the midfielder is not for sale, while manager Ronald Koeman echoed that hardline stance again after victory at Upton Park.
Speaking candidly after the match, Schneiderlin pledged his commitment to Koeman's side while still wearing Southampton colours.
"The situation is I have three years on my contract left," he told Sky Sports News HQ.
"I’m not going to lie about the fact that it was a long summer with a lot of speculation and I was thinking about my future.
"The club refused some offers, they showed me that they wanted to keep me so it’s up to me concentrate and to play my football.
"If the fans or anyone felt that I didn’t respect the club by doing what I did, I want to say that I always respected the fans. They’ve been absolutely amazing with me for the six years that I have been with the team and I have always respected them.
"I just thought about my future. Today my future is at Southampton and if some people are mad at me the best I can do is do my best on the pitch. That’s what I’m trying to do."