The Gunners defeated Bayern Munich 2-0 at the Allianz Arena tonight but exited the competition on away goals after the German giants had won 3-1 in North London three weeks ago.
Goals from Olivier Giroud and Laurent Koscielny gave Arsenal plenty of hope but in the end they came up short, however, Arteta feels it is a result to be proud of even though the overall outcome was not ideal.
"We gave absolutely everything we had in the game. We knew we had conceded three goals at home and it was going to be difficult, but we kept going and we kept believing," he told Sky Sports.
"It was mentally a very difficult game to manage tonight. When we scored the first one they didn't look very convincing and we tried to take advantage of that. We scored a second one at the end and maybe with 10 minutes more we would have had a better chance.
"Coming here, not many teams win here. They have shown that they are a top side in Europe this season, so the lads deserve credit and the boss as well because he believed from the start that we could do it. We tried our best."