Barkley responded with a battling Premier League performance against Middlesbrough, showing a willingness to track back and drove his team forward with his trademark direct running whenever he had the ball.
"Yes, maybe Ross was under pressure but if you don't handle the pressure you can't play in the Premier League," Koeman told British media. "It was an important game for Ross and he responded.
"You can't always say what you think about players but I try to be honest with them... You expect a reaction from the player too. Players are not so stupid that they don't know when they play well or not so well."
Koeman also heaped praise on Idrissa Gueye, who joined from Aston Villa during the close season, and backed the Senegalese to become the best defensive midfielder in England's top flight.
"He was outstanding," Koeman said. "He was perfect in every aspect of football.
"Of course he wins a lot of second balls, he wins a lot of tackles, but the boy showed his composure in midfield.
"He played the ball left, right, always tried to play the ball forward. It's a fantastic signing for the club and I hope we keep him for a long time.
"In my opinion, in that position in the team he will become maybe the best in the Premier League."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
