The former Preston North End boss said that he was happy with his team's workrate, but expressed disappointment about the goal they conceded during the 1-0 quarter-final defeat.
"It is very disappointing as you could probably imagine the players are devastated in the dressing room," he told the club's website.
"The lads gave me everything, they worked their socks off. We huffed, we puffed, we had a couple of chances in the second half, a goal-line clearance, but it just wasn't to be."
Danny Shittu headed the only goal of the game following a contentious corner, but Appleton refused to be drawn into a debate about whether the set piece should have been awarded.
"I think it is debatable but ultimately whether it is given or not, you've got to make sure that you deal with it and you can argue about it later," he added.
"I think it is disappointing the way we conceded the goal. To lose out on a set play in that manner was disappointing."
Millwall will face Wigan Athletic in the semi-finals of the competition.