City stars Kevin De Bruyne and Sergio Aguero both had penalties saved by Everton goalkeeper Maarten Stekelenburg either side of Romelu Lukaku’s opener.
A late equaliser from City sub Nolito earned Pep Guardiola’s team a point but Koeman was delighted with the result due to the quality of City’s team.
As reported by ESPN, Koeman said: “They played fantastic football, good movement, not really open chances because I think the organisation defensive-wise was fantastic of Everton.
“Maybe the goalkeeper played his best game ever -- we know he is a very good goalkeeper -- saving two penalties and two more shots of De Bruyne.
“It is the best team of my managerial career we played against, really high tempo, we make some mistakes because the pressing was so high.
“I’m pleased with the point. We didn’t deserve more, I know. Maybe we didn’t deserve one, counting chances, two penalties missed but football is unpredictable and the key to get a point was the belief and the workrate of the players.
Goal chose to focus on the impact of City goalscorer Nolito and his impressive start to life in Manchester.
Sam Lee writes: “On a day when City’s dedication to playing the percentages so very nearly backfired, Nolito showed exactly why Guardiola wanted him as part of his transitional season at the Etihad Stadium.
“After bossing possession, winning two penalties out of Everton’s mass of bodies and producing two magnificent saves from Stekelenburg, they did more than enough to take all three points.
“As it was, they were left to thank quiet man Nolito.
“His signing did not create the same kind of buzz that welcomed Ilkay Gundogan, John Stones or even young prospect Leroy Sane, but he has done exactly what he needed to do after leaving Celta and, according to the man himself, snubbing Barcelona.
“So often he is in the right place at the right time, and so often when his team-mates are struggling to find space, as they did here today.”
Finally, Sergio Aguero has been speaking to The Sun ahead of the Champions League trip to Barcelona this week. The Argentinian particularly focused on the threat his compatriot Lionel Messi can pose to City.
As Chris Hatherall reports: “I know all about him and of course so does Guardiola – but then when it comes to Barcelona everybody in the world knows about all their players, so it doesn’t mean so much.
“He will be difficult to stop, I know that from experience. All we can hope is that he has a bad day and our defence plays the game of its life. It’s that difficult because Leo is the best in the world.”
That’s all for your round-up today! We’ll have lots of analysis and reaction of City v Everton to come on mancity.com before another round-up tomorrow.