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The Gunners were beaten in the third round by Championship side Forest, who also defeated them at the same stage in 2018.
Those two occasions are the only times in the past 26 seasons Arsenal have exited the competition at the third-round stage.
Forest were worthy winners on this occasion, dominating the game and scoring the only goal through Lewis Grabban in the 83rd minute.
“It is really hurting,” said Arteta. “It is a competition that is very related to our history and to get out of it today is a big bump.
“I’m really disappointed with the performance, first of all. Not with the attitude, but how much purpose we have and what determination we showed to change the game when it’s difficult to play against and the way they play.
“But [we needed] more drive, more hunger to win at any cost in every single action, much more. We were not there at our level today.
“It is frustrating but it happened and you have to analyse why it happened. We can talk about all the players that we didn’t have, which was nine or 10, or the players that we had. And today we should have done something different.
“I know because I have played in games like that for the last 18 years, and I know how complicated it is to come here and it’s no surprise the difficulties that you are going to face. But when we do that, we have to face it in a different way.”
Arsenal were way off the pace in the first-half and Arteta hooked left-back Nuno Tavares after just 35 minutes.
The left-back threw his gloves to the ground in anger after being hauled off, but Arteta said he had to make the change and bring Kieran Tierney on.
“I just needed to try and improve the performance with the team,” said Arteta. “I have to make the decision to try and improve the performance of the team when I see that it is not going in any other direction.”
Arsenal were lacking on numbers for the game, particularly in midfield. Albert Sambi Lokonga and Charlie Patino started there, with the duo the only fit options available to Arteta.
“I want to try to get the best out of the players that we have,” Arteta added. “I think it is clear where we need to strengthen, but at the moment it is what we have. And what we have, we have to play.”