Villa, who trailed 4-2 after the first leg at home, lost 2-0 in Greece to go down 6-2 on aggregate.
On the game, McGinn said: It won't take it away, but our instant feeling is absolutely gutted.
We all wanted to be back here for the final.
Olympiacos gave it absolutely everything, played out of their skin in both legs, and overall the scoreline proves they were the better team.
We'll reflect, there's a lot of things we could have done better, but over the season, of course, we can be proud of the journey.
Obviously, we need to apologize to the supporters who have traveled here, they've traveled the whole campaign with us.
We wanted to deliver a trophy to them, we all wanted it as players. We're all bitterly disappointed, but we need a big push in the last two games to try and get over the line for the Champions League, which would be an astronomical achievement.
But here, the overriding feeling is disappointment, frustration and an opportunity missed.
Congratulations to Olympiacos and we wish them all the best in the final."