Yet there was a sense of what could have been for Guardiola, as City had two clear penalty kick shouts in each half (other than the one Mahrez skied).
City had the flawless opportunity to end their awful run at Anfield but Mahrez, not particularly reliable from the spot, blazed his effort high into the stand.
'The usual taker is Sergio Aguero but he wasn't there.
The result leaves City top going into the global break, but only above rivals Liverpool and Chelsea on goal difference.
Milner, 32, has enjoyed a superb start to the new Premier League season and lined up against reigning champions City on Sunday afternoon.
Arsenal have now won their last nine games in all competitions while the loss leaves Fulham in 17th place, having let in four more goals than any other team in the league. The Reds looked a little jaded midweek in the Champions League encounter away to Napoli, a game which they eventually lost 1-0 after a stoppage-time strike from Lorenzo Insigne. It's not that you go out of a game like this thinking now we have the solution to deal with Manchester City.
On the hour Sterling's corner hit Van Dijk's arm but Atkinson ruled Fernandinho had climbed all over the Holland worldwide, much to the anger of City's bench.
Jesus went down holding his face after a stray hand from Lovren but City's third penalty appeal also went unheard, while Sturridge's weak header was scooped up by Ederson as more half-chances came and went.
"I am so comfortable with the performance we have done".
Pep Guardiola has surprisingly revealed that Manchester City might be able to call on Kevin De Bruyne when his side visits Anfield tomorrow.
"I thought how we defended was brilliant apart from the penalty and one or two situations where we needed Alisson with a really good save". We tried to be ourselves all the time and we compete really, really good. After a challenging run of games, they return to action with an easier period which starts against Huddersfield, Red Star and Cardiff. What few chances there were fell largely City's way.
Referee Martin Atkinson was absolutely right to award Manchester City their penalty in the dying moments.