Rodri secured a late winner deep into added time to secure the win for Pep Guardiola's side.
"You always have two or three games like this in a season. They showed why they are in their position. The way they have grown with Mikel [Arteta] is huge," he said after the match.
"We know they have more rest than us. They have six days to prepare, we have three games in one week and travel. It is tough sometimes, when you don't have the physicality. We have to maybe play a bit more easy.
"We struggled in the first-half but took control in the second a bit more and do more our game. They played a great game but we showed our champions personality."
Arsenal started the game the brighter of the two sides and deserved the lead when it came on 31 minutes.
Things became worse for Arsenal six minutes later when Gabriel was sent off for fouling Gabriel Jesus.
Arsenal were holding on despite their numerical disadvantage but were caught by City three minutes into added time. Aymeric Laporte took a shot which was saved by Aaron Ramsdale but only rebounded as far as Rodri who tapped it into the net.