Olympiacos – who were crowned Greek champions the weekend prior to Wednesday's last 16 second leg tie against Manchester United – failed to capitalise on their momentum.
They threw away a 2-0 lead gained from the first leg, losing the second 3-0 at Old Trafford to bow out on aggregate.
Robin van Persie scored a hat-trick for United, but it was his second goal – that came just before half-time – that Fuster and Dominguez said was the turning point.
Fuster said: "The team are really disappointed. We had high hopes of going through to the next round, but it wasn't to be.
"We started well, we were closing down space, they were struggling to find their front men and we had a few chances which might have changed the game if we'd scored.
"They got the penalty and that made it harder for us, and getting the second goal on the stroke of half-time and then the third made it an uphill battle.
"We still only needed one goal and had to keep trying – we kept fighting till the end but got no reward."
Dominguez added: "The difference was United were better when it came to taking their chances. We had our changes too and didn't convert them.
"It was a game where the narrowest of margins made a big difference. De Gea's save was a key moment but so too was when they got the second goal with 30 seconds left (of the first half).
"I am not satisfied with what we did – we wanted to get through and carry on in the competition.
"We had our supporters behind us, a lot of people followed us here. We did all we could but could not give them something to celebrate."
