Olympiacos triumphed 2-1 in extra-time over Arsenal to progress to the last 16 on away goals after a 2-2 aggregate draw.
Youssef El Arabi netted a dramatic 119th minute winner for the Greek club after Pierre-Emerick Aubameyang had levelled the match in the 113th minute, after Olympiacos won 1-0 in regulation time.
Aubameyang was guilty of a glaring miss in the 123rd minute, which if converted, would have sent Arsenal into the next round.
Instead, Arteta was left to rue missed chances, finishing with 19-12 shots and 61-39 per cent possession advantage.
“I think as the game went on, we were getting better and better and they were playing deeper and deeper,” Arteta said.
“We generated more than enough chances to win the game and we shouldn’t be talking about what happened now.
“I think we have enough goal threat in this team, but we have to put the chances to bed and in Europe its in both boxes.
“In the opponent’s box, we missed chances that should have been goals and in our box there were a few things that they had and they put them in.”
Both of Olympiacos’ goals came from set-pieces, with Pape Abou Cisse heading home from a 53rd minute corner and El Arabi sliding in from a short corner.
“On the set-pieces we were vulnerable again so these are things to improve,” Arteta said.
“Details are so important in ties. We gave details away that you cannot afford. Even if not in the opposition box, you have to be ruthless, and we weren’t tonight.”