Arsenal were beaten on penalties after the scores finished 1-1 following extra-time. United also had Diogo Dalot sent off midway through the second-half.
Arteta later said, "It's unbelievable. Obviously, you measure the performance and what we did in relation to the position, you-know, you deserve to win the game by a mile.
"But the reality is we are out and the only thing that's going to be judged it that but internally I can't.
"I love my players. I love our team and I love how good they are and what they do because in 1000 games, you should lose one and probably it was this one. You have to understand this as well, it's part of our industry, our game and move on because you don't have time to do that because on Wednesday we have a massive one.
"It's football and it is a part of that education, you need things to go your way and tonight it didn't.
"When you go to penalties you know that it's a flick of the coin and it can go either way.
"It's an incredible team. I'm so proud of my players. I love my players and I cannot be prouder because it's very difficult to demand something else than the performance that they put in there.
"The ball has to go in the net and then you have to batter the opponent, that's the reality."
On Gabriel Jesus going off injured, he added: "No update but it's not looking good. He was in quite a lot of pain, he had to come off on a stretcher and he's not looking good."