The Gunners fell to a 2-1 defeat to the Spanish side in the first leg of the semi-final but Arteta was relieved that his team have a fighting chance to turn the tie around in next week's return leg.
He said: "Obviously we are disappointed that we lose the game because it’s not the result that we wanted to take from the game.
"But after the story of the game we have to take it because we are in the tie, we are alive and the circumstances that were in the game put the game and the tie in real danger."
Arteta was questioned for his team selection after not starting with a recognised striker but the Arsenal boss lamented how his team "disorganised" themselves.
He said: "After conceding the goal we disorganised ourselves.
"In the high press we were really stretched and we didn’t have the right spaces with the right people and then we were open.
"We didn’t give ourselves the chance to get set in the final third to do what we wanted to do because we were not precise on the ball as well.
"Overall, it wasn’t the best, we started the second half in a completely different way. We’ve played with three strikers sometimes and we didn’t score any goals many times this season. It’s a decision I made and that’s it."