The 35-year-old started the impressive 3-1 win over Middlesbrough at Goodison Park, capping his strong performance with the equalising goal for the Toffees.
Barry, who previously played for Aston Villa and Manchester City, has started the season in fine form, and Koeman told talkSPORT the veteran is showing his talent in every aspect of his game – whilst also praising midfield teammate Idrissa Gueye.
When asked about Barry’s performance, Koeman told talkSPORT: “Very pleased. Of course it’s an amazing number of games, 600. And he showed today he is still in charge, not only to score to make it 1-1, but in all the aspects [of his game].
“The other key player was Gana in the midfield.”
Boro took the lead at Goodison Park, Maarten Stekelenburg putting through his own net after he was clattered by Alvaro Negredo.
It looked a foul, but the goal was given, although Koeman believes it was going behind which kicked the Toffees out of a stupor and forced them to find their best form.
He added: “I was very pleased for about 75 minutes in the game, because I think the start was not good; we were not that aggressive.
“But after that [the Middlesbrough goal] there was more pressing and we were more aggressive; we won more second balls and played good football. And we turned around the 1-0 score.”
Koeman also provided an update on Romelu Lukaku, who was taken off in the second period with an apparent injury.
“[It was] his feet, not his ankle. We have to wait, and tomorrow we will know something more.”