The Hoops were eliminated from the competition in the fifth round despite scoring early through Anthony Stokes as goals from Russell Anderson and Peter Pawlett sent the Dons through to the quarter-finals.
"Defensively and midfield-wise we were second best," Lennon said.
"It's very difficult to single out any player with any credit - Stokes possibly and James (Forrest) maybe had a spark but the rest of the team were very flat.
"That is as poor as we have played for a long, long time. There was a flatness about our play today and I don't know where that has come from. It's in our DNA as a club - we want to defend the Cup.
"There was no excuse for today, that was a poor performance and we have to accept the criticism that will come our way.
"But you have got to give credit to Aberdeen, they came here with a game plan and it worked out well for them."
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