Arteta's side finished two points behind City, after their 2-1 win over Everton on Sunday was rendered irrelevant by a 3-1 victory for Pep Guardiola's men against West Ham.
Failing to end their 20-year title drought on the last day of the season meant Arsenal have finished as runners-up to City in successive campaigns.
But a visibly emotional Arteta issued a rallying cry to the club's heart-broken players and fans during an on-pitch address immediately after the match.
"All this is happening because you started believing," the Spaniard said.
"You decided to be patient, you decided to understand what we are trying to do and all the credit has to go to the team, the players, the staff. It is unbelievable.
"Now it's time to have a break. Think, reflect and please, keep pushing, keep inspiring this team.
"Don't be satisfied because we want more than that and we're going to get it."
Kai Havertz scored Arsenal's 89th-minute winner, but the German's goal came too late to give his team a miraculous title triumph.
Havertz admitted the last-day disappointment left a bitter taste, especially after they stormed through 2024 on a superb run that featured just one league defeat against Aston Villa.
But he echoed Arteta, vowing that Arsenal would be stronger after the pain subsides.
"I feel sorry for all the Arsenal fans, for us, we gave our best but it wasn't enough," Havertz said.
"Maybe in two or three months we can say 'it was a good fight', but right now I feel like we deserved more. It wasn't enough in the end, but we go again next year.
"Sometimes it's not fair in football, but we have to accept it. Football is hard, but hopefully we can go again next year and give the Arsenal fans what they need.
"It's frustrating. When you see all the fans here it's tough, but I can tell them next year we're going to be an even better team."
