The Frenchman will stay at St Mary's until January at least, despite reportedly trying to orchestrate a move to Tottenham Hotspur in the summer window.
"I was blocked but I must accept that because I have three years remaining on my contract," The Express quotes Schneiderlin as saying.
"I could not afford to make a fuss and not play. I owe a lot to Southampton, who enabled me to make the France national team. I could not afford to go and clash with supporters who have always been cool with me."
The midfielder has scored two Premier League goals three games into the season.