The champions needed a John Stones equaliser deep into stoppage time to escape with a 2-2 draw against 10-man Arsenal at the Etihad Stadium.
Arteta's side, runners-up to City in the Premier League for the past two seasons, had Leandro Trossard sent off just before the interval.
The Gunners did their best to deliberately disrupt their rivals with time-wasting and cynical fouls in the second half.
City struggled to break down Arsenal despite dominating possession, leading Stones and teammate Bernardo Silva to accuse the north Londoners of resorting to football's 'dark arts'.
Arteta, who worked as Guardiola's assistant at City before becoming Arsenal boss, said the controversy would not get in the way of his personal relationship with his fellow Spaniard.
"I love him, I respect him and I admire him, his team and everything that he does," he said Friday, on the eve of his side's match against Leicester.
"This is a sport - one thing is our profession and the other is our personal relationship.
"If my relationship has to be damaged because we play against each other and one draws or the one wins, or the amount of times that we have lost then I wouldn't talk to him any more."
Arteta was asked by reporters whether it was harder to maintain a friendship when games between title contenders are so ferocious.
"It's quite simple - don't take it personally, it's part of our job," he said.
"The things that you really care about, make sure you handle them in the right way.
"That relationship, I really care about. It's the same with a lot of people in their staff and players that I spent some very important years of my life with."
Unbeaten Arsenal are fourth in the table, two points behind City, who are top of the pile after five games.
Arteta, whose team meet Paris Saint-Germain in the Champions League next week, said he was unsure whether goalkeeper David Raya would be fit to face Leicester after picking up an injury against City.
"We have to wait 24 hours to see if he's looking good or not that good," he said.