Koeman decided to take Barkley off at half-time during Monday's Premier League contest at the Stadium of Light, which was goalless at the break before the Toffees ran out 3-0 winners.
The Dutchman later said the 22-year-old England international "didn't show the level" expected of him
And, speaking on Thursday ahead of Everton's home clash with Middlesbrough on Saturday, Koeman stressed Barkley needs to up his game "in all the aspects".
He said: "If you play a match, you analyse it, and of course there was a reason to change Ross at half-time - because he did not play well.
"He lost many balls and a player of that quality can't lose those kind of balls.
"We always analyse the game, and then you have individual talks, and of course I had an individual talk with Ross.
"He needs to improve, but okay - we will see at the weekend."
Put to him that Barkley's drop in performance level might be linked to him being left out of Sam Allardyce's first England squad last month, Koeman said: "In my opinion, that is the past - what counts now is what happens now.
"I mention always that you get game time in national teams because you play at a good level for your club, and it is deserved.
"That was one game, what happened on Monday.
"I spoke to him and he understands - because we showed the clips, and then there is no escape."
Koeman added: "I think it is the more the way how he used to play.
"The player is strong enough to work harder to do better pressing
You look to his qualities and he needs to be the key player between defenders and strikers - he is that position in the midfield, to create, but also defensively to be part of the team.
"In all the aspects he can improve - and he needs to improve
But he still a young player, no question."
Meanwhile, Koeman has been full of praise for Barkley's midfield colleague Gareth Barry, who is set to make his 600th Premier League appearance in Saturday's game.
"He will be selected, and it is amazing, fantastic," Koeman said of the 35-year-old.
"He's still an important player for us because he is a clever player.
"You have to minimise the training intensity a little bit across the whole week to keep the player fit to play.
"I'm very happy that he's still part of our Everton team."
Barry's current contract runs out next summer, and when asked about a possible extension for the player, Koeman said: "We will speak about that.
"Not today, not next week - but, of course, if he is still that player we need, then we will start talking about next season."
Source : PA
Source: PA