Saturday's tight fourth-round tie swung Rovers' way a minute before half-time when a mistake by Richard Keogh allowed Colin Kazim-Richards to break the deadlock.
Quickfire goals from Scott Dann and Jordan Rhodes in the second half saw the visitors ease to a 3-0 victory.
Several Derby players were called up to various national teams last week, but Blackburn boast established international players throughout their side, including Kazim-Richards, Rhodes, Grant Hanley, Morten Gamst Pedersen and Danny Murphy.
And Clough admitted his side found it tough, saying: "There wasn't too much between the two sides until the opening goal, which was a sucker punch for us just on half-time and it certainly gave Blackburn a lift.
"Their quality shone through in the second half and they also made very few mistakes at the back, so when they got two quick goals just after the hour it killed off our hopes of getting back into the tie.
"It wasn't our day and it's tough for the young lads, but they shouldn't be too despondent because they've all had a great first half of the season.
"They were up against international players and sometimes they will learn more from a defeat than they would from a victory, especially in both penalty areas.
"Although they might not feel great at the moment, it's a big learning curve for them when they experience disappointments like that."