Regardless of Arsenal’s result at Nottingham Forest next Saturday, City will be champions if they win any one of their final three matches.
“A really different feeling to the feeling that we all had last Sunday [against Newcastle] when we felt proud and we felt that we really did what we needed to win in certain moments,” said Arteta.
“Today is completely the opposite. We have to apologise to our people, especially for the second half. What I have to accept first is what happened in the second-half and digest it. Look individually at what happened in the second-half.
“The second position is secure. That’s not going to change. We have to digest and that will take a few days. I’m responsible for what happened today. My job is to get the best out of every single individual that we have.
“And if we have to take it there (pretends to shoot himself) for 10 and a half months, we have to and they have too. I have tried to do that with my best ability but today obviously I didn’t do it.”
Arsenal were outplayed by Brighton for much of the game on Sunday, with the visitors dominating possession.
Julio Enciso opened the scoring and after that Deniz Undav and Pervis Estupinan wrapped up the win late on.
Arsenal have enjoyed a brilliant season, leading the League for over 200 days, but asked for his emotions now, Arteta said: “At the moment it’s just frustration.
“The feeling that we gave the game away in the second half. We fought really hard to be in the position that we are in and today we were in a critical moment to keeping hoping and digging for that dream.
“When you have to play in these moments you cannot do what we did in the second half. Then we have to look. If a team is capable of doing that when it comes to the biggest stage, there’s a lot of things to analyse and think about because it cannot happen.”
City are now on course to win the title after Arsenal’s loss on Sunday and Gunners captain Martin Odegaard admitted it felt like their race is now run.
“It looks difficult now to be honest, we have to be realistic,” he told the BBC. “I don’t think City are going to do too many mistakes now.
“We just need to get back on the pitch and end the season in a good way. I think everyone deserves that, especially the fans.
“We did okay in the first-half with the high press and could have been dangerous and scored some goals.
“The game changed a little bit in the second-half, when they went direct it was a bit too easy for them to get through. I don’t know why at the moment. I don’t have any answers.
“We’ve done a lot of good things but at the moment it is just disappointing how we’ve ended. It is a good sign that we are disappointed. We just have to make sure we keep improving and getting better.”