The Reds were beaten 1-0 at Old Trafford by the Spanish club, who progress to the quarter-finals 2-1 on aggregate after a draw in the away leg.
De Gea was frustrated against his former club, even going up for an injury-time corner in a desperate bid to grab an equaliser.
Speaking to MUTV and BT Sport following the full-time whistle, David said: “We are really disappointed with the result.
“Obviously, it's difficult to describe in words how we feel now at the moment, but we did not do enough in both games to win both games.