Arteta said: "At the moment it's a gutted dressing room, very disappointed. I cannot find the right words to leave them, I wish I had.
"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. 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, 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."
On if Arsenal missed a moment of magic, he continued: "Yes. Had to be. A mistake from them or a magic moment, that is what unlocks the tie. We didn't manage to win it at the end and we could have won. At moment 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.
"The club has been without Champions League football for seven years. The first time you want to be in it, then you want to be in the semi-finals and finals. We all want it so badly, but you see in many other clubs it takes six, seven years to get to that stage. But we were very close, that is the reality."
On the title race, he added: "What we have ahead is beautiful. Six games to and we are two points behind City. A busy schedule for everybody. We have to go through the pain tonight, and tomorrow get up, come with the same attitude that we came here and hopefully beat Wolves."