After watching a number of key players leave early in the summer, the Saints rejected a request from the French midfielder to sanction a move, which was a decision that sparked an angry reaction before the start of the season.
However, Schneiderlin is once again a key member of the Southampton side, and Koeman is delighted to still have the 24-year-old in his squad.
"I hoped, and in the last three weeks I would say yes, him staying has been the best part for us," the Saints boss told reporters. "He's a fantastic player and an important player for the team. That gives the rest of the lads confidence and ambition.
"It was not an easy one because he was disappointed in the beginning, but I think that was a normal reaction.
"But, after that, his behaviour has been professional and the one answer he gave was on the pitch, and that's always the best answer that you can give."
Schneiderlin and Southampton return to action against Newcastle United on Saturday afternoon.