“We are still not on the right level and we have seven points out of nine”
It was not all good news for Everton, however, as midfielder James McCarthy may have to have surgery on a groin problem which ruled him out of the match but, regardless, he will not be sold in the transfer window.
“We need to decide if it is an operation, yes or no,” added Koeman.
“There is more interest in players of Everton and we like to keep everybody and players like McCarthy need to stay.”
Koeman handed a first Premier League start to new centre-back Ashley Williams and also winger Yannick Bolasie.
But it was a defender at the other end of the pitch who caught the eye.
It was not really a case of trying to stake a claim for a long-awaited England recall in front of new boss Sam Allardyce, as Ryan Shawcross has been playing like this for most of the time he has been at Stoke.