Mikel Arteta said he was in "shock" and branded Arsenal's performance in their 3-0 home defeat by Liverpool as "unacceptable".
The Gunners, nine points off a Champions League spot with eight games left, were outclassed as they conceded three times in the second half.
"They were much better than us in every single department. I'm fully responsible for that," said Arteta.
"We want to apologise, to our people and our fans."
The Gunners are ninth in the table and their only realistic hope of securing a Champions League place is by winning the Europa League.