Gabriel Jesus scored both goals in the space of seven second-half minutes at the Etihad Stadium but what could have been a comfortable win became tense after Claudio Bravo gifted Everton a reply.
City boss Guardiola was pleased that the Premier League champions, whose title defence looks over after falling well behind Liverpool, overcame fatigue to dig in to get a result from their third game in six days.
Guardiola believes many teams would give up, considering they are so far off the top, but that is not the case with his side who will continue to fight for the remainder of the season.
Asked how his team played, Guardiola said: "Really well. We played top. I'm so delighted about the performance and behaviour as always."
Richarlison pulled one back for the visitors after Bravo turned an Everton forward in the box but then passed straight to another.
Guardiola did not condemn the goalkeeper who was handed an unexpected chance to start after Ederson fell ill.
Guardiola said: "It happens when you play in that way but thanks to him we can make a build-up better and use long balls. It happened, it's football, but always I encourage them to do it."
City had a Phil Foden goal disallowed by VAR in the first half, with Riyad Mahrez found to be offside in the build-up, much to the frustration of the home fans.
Guardiola, however, had no issues with the decision, saying it was correct.
However, he was in little doubt Dominic Calvert-Lewin should have been sent off for a poor challenge on Fernandinho, for which he was only booked, in the closing minutes.
However, the incident drew a different response from Guardiola's opposite number Carlo Ancelotti.
"Pep knows it was not a red card," said the Italian. "It was a strong tackle but he went on the ball, so I think it was the right decision."