Goals from James Henry, Rob Hulse and Dany N'Guessan ended the non-league side's hopes of progressing past the fifth round.
"They always give their all this group of players," said Buckle.
"Every player I have tried to sign has to have them qualities and they gave their all right to the very end.
"The biggest disappointment today was not scoring a goal because I really felt, with the chances we had, we deserved a minimum of one goal.
"The dream is over and it is disappointing because of the manner we've gone out, really.
"As professionals, we've gifted it to Millwall. We really have given them a leg up that they would have loved to have had.
"They were professional, cleared their lines and did the nasty side, but what we did never gave us a chance to put them under pressure.
"But listen, it has been an unbelievable cup run. We've done great. I really thought we could get to the quarter-finals, but maybe next time."
Buckle is now hoping to lead Luton back into the Football League, although they are currently nine points adrift of the Blue Square Bet Premier play-off positions.
"What we've got to do is get as happy and buzzing about the league as we have been in the cup," he added.
"We have to understand that this great football club I am manager of is a non-league football club.
"As much as that hurts, that's the truth. To get out of this division, we've got to show some real fight, spirit and character and a lot of togetherness."