Raheem Sterling’s first half goal was enough to condemn Arsenal to their second defeat of the season.
The Gunners fairly matched the hosts throughout the game and could have gotten at least a point if not for their own profligacy.
Arteta was speaking to the media after the game and he admitted his side should have taken their chances against the Citizens, but remains optimistic about the potential of his team.
“We created some big opportunities, maybe two or three, and we have to convert them if we want to win matches like this,” the former midfielder said.
"We didn't, but apart from that the belief I sense in this team made me very proud.
"I have seen a lot of teams come here in four years working here. So I know to do what we did tonight is really difficult.
"Overall I cannot be any prouder. If we have to lose football matches, I would prefer to lose matches like this. So I can take a lot of positives, but I hate losing."
His counterpart Guardiola also reflected on his side’s big win against one of their Premier League rivals, and singled out some of his best performers against Arteta’s men.
“It was difficult but we have won 1-0 and Ederson again was incredibly active like he was against Leeds.”
“We are still little bit away from our best performance that we are wishing but for many reasons it is not possible.”
“The victory helped us a lot, we defended really well deep and up front and a good three points against an impressive opponent.
"Arsenal have two or three more weeks preparation in pre-season which we did not have. Bernardo Silva and Joao Cancelo came back from injury, four players from Covid could not train, Ilkay Gundogan was 15 days off and is still far away and that is why we are a little bit away from where we want to be.
"Nathan Ake was incredible, Ruben Dias as well. The way Arsenal attack, we needed Kyle Walker's speed to control Pierre-Emerick Aubameyang. Nathan knows his job perfectly, he does not make mistakes and this happens because he is a nice guy. Nice guys always play good, that is my theory.
"We are so happy with Sergio Aguero, he was out for four months but is a guy who need rhythem, I am so happy for him he is back."