Following a 2-2 draw in last week's first leg at the Emirates, where the Gunners were left to lament uncharacteristic defensive sloppiness, Arteta's side were made to pay for falling asleep in the box at the Allianz Arena.
While struggling to unlock an indestructible Bayern defence - marshalled by the sturdy pairing of Matthijs de Ligt and Eric Dier - the fatal blow arrived from Joshua Kimmich, who ghosted into the box in the second half to head home from Raphael Guerreiro's delivery.
Barring a Gabriel Martinelli strike which fell straight into Manuel Neuer's gloves and a Martin Odegaard effort which was tipped behind by the goalkeeper - and inexplicably preceded a goal kick - Arsenal severely lacked penetration in a performance akin to the weekend's Premier League loss to Aston Villa.
Throughout the second 45 minutes, Arsenal only chalked up a paltry three shots for an expected goals total of 0.15, and they have now lost back-to-back games without scoring for the first time this season.
Arteta: 'There was zero margin for error'
On the back of Arsenal's latest Champions League elimination at the hands of Bayern, who have now beaten the Gunners on eight occasions, Arteta conceded that one huge blunder was responsible for his side's excruciating exit.
"At the moment it is a gutted dressing room. We are very disappointed. We have to go through it. We tried against a team with a lot of experience. Through the tie the margins have been very small," Arteta told TNT Sports.
"There were moments that we were better, we gave them two goals - that is a big advantage to give away. Today you could see that it was a zero margin of error. We made a mistake defensively in the box, a big one, and we give away the goal.
"Now is the moment to stick with the players, because they need our support. They are the ones that have taken us on this journey. Had to be a mistake from them or a magic moment and that is what unlocks the tie.
"We didn't manage to win it at the end and we could have won. At moments we were better than them and had a lot of moments of dominance. That spark around the box is what you need in these ties to get the victory."
Arteta makes "10 years" Champions League admission
After multiple failed build-up sequences, Arsenal were presented with some golden chances to threaten the Bayern penalty area with a couple of late set-pieces, one of which saw Leandro Trossard fail to deliver the ball into the box after Declan Rice's short free kick.
With seconds remaining, Bukayo Saka then curiously opted for a quick free kick in a promising position, but Bayern snuffed out the danger, before the resulting corner from the 22-year-old failed to beat the first man as the final whistle sounded.
Fourteen years on from Arsenal's last Champions League semi-final appearance, Arteta conceded that some sides have taken a decade to progress as far as the final, telling a press conference: "We haven't played in the competition for seven years; we haven't been in this position for 14 years.
"We have to learn it, when you look historically, all the clubs to get to certain stages, it took them seven, eight, some of them 10 years to do it. Today that is not going to make us feel better, that's for sure."
Now only scrapping for Premier League supremacy, Arsenal are back on the road on Saturday evening, facing Wolverhampton Wanderers with the chance to rise back to the summit of the table as Manchester City turn their attention to the FA Cup semi-finals.