The Dutchman is looking for more from the wingers.
Both players are looking to bounce back this season after frustrating campaigns under Roberto Martinez last season.
Mirallas in particular is determined to make his mark having fallen out with the Spaniard and lost his place in the first team for much of the campaign.
Everton's Gerard Deulofeu in action with Tottenham's Toby Alderweireld
They were both handed starting roles in the first game of the season on Saturday as the Blues drew 1-1 with Tottenham Hotspur at Goodison Park.
And Koeman has insisted he likes both players, but they must run and press more to be a success in his team.
“You see with Gerard it is still not for 90 minutes,” he told the Liverpool Echo.
“With Gerard, with Kevin, I like the players but they need to run more. They need to do more, they need to press more. It’s all about the work rate of the player.”
Kevin Mirallas celebrates scoring the second goal for Everton
It will now be interesting to see if both players can flourish under Koeman at Everton this season.
They were both put in decent performances in the draw with Spurs, but will know it will take more than one solid display to earn a place in this Blues team moving forward.
Clearly their new manager wants to see more and it remains to be seen if either can find that next level to please the Dutchman.
Everton manager Ronaldo Koeman