The Gunners went out in the third round at home to Manchester United on Sunday.
After a 1-1 draw in normal time, Arsenal could not score in extra time despite United having ten men.
After losing the penalty shootout, Odegaard stated: “It’s a really tough one.
“Really frustrating. I think we completely dominated the game from the first half until the end. We could have been a bit sharper in front of goal, in the last pass, the last shot. To lose that game at home when we dominated everything, it’s a tough one.”
He added: “It’s hard to say at the moment exactly why, but I think it’s small details; the last pass, the finish, the decision-making. Again, I think we did more than enough to win this game – I don’t know if they had a better chance than the goal and we created enough to score. Me with the penalty as well, that should have been a goal.
“It’s not good enough from me, I have to score that one. I think it was a crucial moment as well, so it was a tough one to take. That’s it.”