Arteta’s side crashed out 5-3 on penalties in an incredible fourth round upset after the tie finished 1-1 in normal time.
Arsenal’s Bruno Guimaraes had his penalty saved by Jay Lynch in the shoot-out and Conor Haughey scored Fleetwood’s winner.
Aaron Loupalo-Bi’s first-half goal had put Fleetwood ahead before Viktor Gyokeres equalised after the interval.
Arsenal’s 16-year-old rising star Max Dowman was sent off for violent conduct in the closing stages.
Arteta paid the price for prioritising Sunday’s Premier League trip to Liverpool as his decision to make nine changes backfired spectacularly.
The Gunners boss conceded Arsenal could have no complaints, admitting it was a painful moment in his reign.
“First of all, congratulations to Fleetwood for going through the next round. The manner that they have done it, and for us a very sad day,” Arteta said.
“There is nothing to criticise the players for their attitude, their application.
“The determination, you could see that was there from the start, even with 10 men. But we conceded a really poor goal to start with that gave them some momentum.
“Obviously we have so much of the ball, so many chances, so many shots, and if you want the margins to be bigger than going to the penalties, you need to capitalise on that. And we didn’t.
“It’s football, that’s the beauty of this competition. It’s a very sad day.”
Arsenal had moved level on points with Premier League leaders Manchester City after a 2-0 victory over Everton on Saturday.
But instead of extending their run of 11 wins from their 13 previous games, Arteta’s team returned to north London red-faced after a loss that ranks among the darkest days in the club’s glittering history.
“Zero problem attitude-wise. Otherwise, I would be here absolutely fuming. I’m sad, I think we are all sad. We have a massive responsibility to carry this badge in the best possible way,” Arteta said.
“You don’t capitalise, then you cannot go through to the next round. Unfortunately, we are out.”
– ‘I just can’t believe it’ –
Although it looked a harsh decision to send off Dowman for aiming a kick towards Harrison Neal, Arteta was unimpressed with the 16-year-old, giving him a stern word as the midfielder trudged off.
“Something that we discussed already before the match,” Arteta said when asked what he told Dowman.
“It’s difficult to see on the cameras like that, so I prefer to watch it back properly and then I can assess the situation.”
Fleetwood made a mockery of the 84 places between the clubs in the English football system with a defiant display that stopped Arsenal establishing any momentum.
Their refusal to be overawed by Arsenal’s star-power was a tribute to Fleetwood boss Matt Lawlor, who won the tactical battle with Arteta by sitting deep and attacking on the counter.
“I just can’t believe it. The biggest night in the club’s history in terms of opposition coming to town and we’ve managed to beat the champions,” Lawlor said.
“We’re not stupid enough and not egotistical enough that you think we’re going to out-play the best team in the country and the most organised team in the country.
“So we had to ride our luck, we had to deny space, we had to deny options for them. And I think we did that really, really well in terms of the majority of the game.”
While Lawlor was composed during the match, his emotions poured out in his tearful celebration as jubilant Fleetwood fans invaded the pitch after the winning penalty.
“I’m just so glad that the lads have the feeling the way they are and took that performance into make that town, the club, everyone proud,” he said.
