The home side had the most possession and over twice as many shots, but Greece claimed the victory.
The 31-year-old was marking Greece's goal scorer Jose Holeban in the run up to his goal.
After the match, the Manchester United player told Sky Sports News: "For the goal, I should have done better. I let them off too easily, but we should have already been a goal up by then.
"We would have like to have picked up a win tonight to have given everyone a boost."
Ireland had a number of penalty shouts throughout the game, including one in the opening minute, where replays showed that Konstantinos Stafylidis handled the ball.