Lifting three trophies at Manchester United last season was not enough to satisfy the 31-year-old, whose frustration at a lack of regular first-team football grew under Jose Mourinho.
Rooney took the decision to leave Old Trafford after 13 medal-laden years and in the summer rejoined Everton, who he inspired to victory on his first Premier League appearance for the club in 4,837 days.
The forward nodded home at the end of a fine team move late in the first half to secure a 1-0 win against Stoke and impressed with his all-round display at Goodison Park.
"He shows that he's still one of the best in his position," Koeman said, lavishing praise on Rooney. "I think he was different class in ball possession - he was comfortable on the ball, he took right, good decisions on the ball and he scored a great goal.
"And you cannot ask more (than) that."
Asked if he brought to the team exactly what he wanted, Koeman told broadcasters: "Yeah, that's what you like. You like to have players in the team with a lot of a cleverness on the pitch and that they know, they see and they handle what they need to do at a certain moment. That was his best game so far."