The north London side are facing the prospect of missing out on European football next season for the first time since 1996 as they battle to finish in the top half of the Premier League.
Arsenal were knocked out of the Europa League at the semifinal stage on Thursday night by Villarreal, managed by Arteta's predecessor Unai Emery, and pressure is mounting on the 39-year-old after a hugely disappointing campaign.
Trailing 2-1 from the first leg, Arsenal drew 0-0 at Emirates Stadium as captain Pierre-Emerick Aubameyang hit the post with a late header, but the end result was a new low that continues a slide from being Champions League regulars under Arsene Wenger.
"I understand [fans'] concerns because when you are out of the Champions League for five years it is not just a casualty, it's a trend," he said.
"There are facts to support that trend. So, there are things to change, that's for sure because you know no one is going to accept that at this football club. I am not going to accept that, and the fans are not going to accept that. So we all have to push together to achieve something very different."
Asked why that trend was occurring, Arteta replied: "They are things to analyse more internally, I am sorry. We have done that. There are things that we cannot discuss here. I take full responsibility for my part, for sure, since I arrived here what I have tried to do, giving my life, my best ability, investing every drop of energy that I have emotionally to support everything that has been going around with my knowledge, with staff, with all the players that are trying to contribute with all the club to give our best.
"But so far it has not been enough and this is when the question mark comes: why it is not enough? Is it just a thing? Is it the manager? Is it other stuff? What is it? And then this is football. Last night that ball goes in, we win 1-0. You are in the final and it is a different world. But today that world doesn't look very nice."
Sources have told ESPN that the Arsenal hierarchy are disappointed with the end to the campaign but remain keen to continue supporting Arteta, who has been instrumental behind the scenes in streamlining the squad, persuading young players Bukayo Saka and Folarin Balogun to sign new contracts while also helping negotiate an initial 12.5% pay cut for the first-team squad to help offset the financial impact of COVID-19.
"What I felt last night was a deep pain because the moment the club is in at the moment, with everything it has been through over the last months, I had a feeling that if we could take the team to the final, it could be a great turning point," Arteta said.
"I felt that responsibility and I was so eager to achieve that because I knew it could be a defining moment. Not being able to achieve it has been really tough personally obviously. I know that we have disappointed a lot of people as well, and that really hurts because we want to give the best to everybody, but one thing I made clear is that to do what we want to do, I have no doubts that we are going to achieve it. If not, I wouldn't be sat here."