Steve McClaren praised his side after Derby lost 2-0 to Chelsea in the FA Cup third round at Pride Park on Sunday.
The Rams held their Premier League rivals until the 66th minute when John Obi Mikel slotted home, with Oscar adding a second five minutes later.
The defeat means Derby, currently fourth in the Championship, can concentrate on gaining promotion back to the Premier League.
McClaren said: "(I) couldn't be more proud of them. We played against one of the best teams, not just in the Premier League, but in Europe.
"(We) started the game well, finished the game well, just that five-minute spell, with the two goals, were the disappointment of the afternoon."
McClaren knows the gap between the elite and the next level is increasing, but it is not yet too big a concern.
He added: "The gap is getting bigger, but teams, (but) you worry about it when you get there.
"You saw today that the difference in level is huge. Their front four are quality players, but they pay a tidy sum for them.
"We're just getting young players and developing them."
Between the two goals, Ramires was booked for diving after he went down under the challenge of Michael Keane, although McClaren said he did not see the incident as he was moving from the stand to the touchline at the time.
He said: "I didn't quite see it. That happens. The pitch was slippy, maybe he just fell over."