The Gunners had topped the table for much of the season as they tried to end a 19-year wait to win the title. But under relentless pressure from City, who have won 11 consecutive league games, the wheels have come off for Arsenal in recent months.
"We have to apologise because the performance we had in the second-half is not acceptable," Arteta told 'Sky Sports'.
"Mathematically [winning the league] it's still possible and this is football but today it's impossible to be thinking about it. We have to first digest the result, the performance that we had in the second half, and understand why and have a very different reaction in the next game."
City will win the title for the fifth time in six seasons, and for a third year in a row, if Arsenal lose at Nottingham Forest on Saturday. Even if Arteta's men respond at Forest, the title will still go to City if the leaders win at home to Chelsea on 21st May or take three points in their other two matches at Brighton and Brentford.
Arsenal have surpassed expectations just by being involved in the title race and they have secured Champions League qualification for the first time in seven seasons. But Arteta said his side's failure to respond after falling behind to Julio Enciso's header early in the second-half is a red flag ahead of next season.
Deniz Undav and Pervis Estupinan rubbed salt in Arsenal wounds in the closing stages as Brighton took a huge step towards European qualification for the first time in the club's history.
"We concede a goal and from there the team had no reaction. When you give away the silly goal we gave away, the second one, the team collapsed and had no answers. If the team is able to do that there is something we have to address," added Arteta.
May 14, 2023