Raheem Sterling's early header proved decisive as City extended their winning streak to 18 matches and Guardiola was satisfied with the tight nature of the win.
He said: "Every game you are not going to win games 2-0, 3-0, 4-0, sometimes when you win 1-0 it is so good. We have to realise what we are doing is so difficult. It is a struggle, a fight, behind the ball and that is why we like this result."
The Spanish coach admits that he was happy that his team were able to overcome the Gunners - managed by his former City assistant Mikel Arteta.
Guardiola told BBC Sport: "They are aggressive with one-to-one pressing. They move really well in the pockets and speed from the sides. It's so difficult to play against. We knew today would be one of the toughest ones but we scored early and we could control it.
"Of course, we could score the second and the third but we scored then they defend well. It's so difficult to play Arsenal and Mikel [Arteta]. He knows our players so well. It is not easy to play and we play so, so calm and intelligent. It was a good game."
City maintained a 10-point lead at the top of the Premier League with the win but Guardiola is focusing on one match at a time rather than dreaming of glory.
He said: "We think all the time the next one. That is now Champions League, then West Ham at home. One at a time. 39 points to play. We have 10 up front. So we have to win."