Arsenal effectively ceded control of the title race after Manchester City had earlier dispatched Everton 3-0 at Goodison Park.
Pep Guardiola's side will win the title for the third straight season if they beat Chelsea on Sunday or Arsenal lose to Nottingham Forest on Saturday.
Hopes were high at the Emirates Stadium when Arsenal topped the table for much of the season but a dismal run which has seen them drop points in five of their last seven matches handed the initiative to City.
“A really different feeling to the feeling that we all had last Sunday (at Newcastle) when we felt proud and we felt that we really did what we needed to win in certain moments. Today is completely the opposite,” Arteta admitted.
“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.
“After that until it’s mathematically over… the second position is secure. That’s not going to change. We have to digest and that will take a few days.
“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.”
Arsenal's consolation for missing out on the title is a return to play Champions League football for the first time since the 2016/2017 season.
