Schneiderlin has been linked with a switch to Tottenham throughout the close-season and vented his disappointment at Southampton's spate of player sales on Twitter.
But Koeman claims the 24-year-old – who represented France at the World Cup earlier this year – has changed his mind on his future with the club.
Southampton started their Premier League season with a 2-1 defeat at Liverpool on Sunday, with Schneiderlin playing the full 90 minutes.
And although Koeman acknowledged he was rusty, he thinks Schneiderlin has an integral role to play in his new-look Southampton side.
"I think it was good for him [to play]," Koeman said on Sunday.
"You saw it in the last 10 minutes… that he was tired because it was his first match.
"But the competition is starting today, yesterday for the rest, and he is a player of Southampton. He [will] continue playing for Southampton.
"He changed his mind, he changed his mentality, he showed us that last week. He is a key player.
"He shows qualities today, he is strong, he is a good football player. He is very important for our team and it was normal for me to put him in the line-up."
