Chesterfield caretaker manager Tommy Wright - who refuted speculation he has been handed the role on a full-time basis - was frustrated with the manner in which his players' Johnstone's Paint Trophy defence was ended.
Doncaster dominated possession throughout the game with short, sharp passes and were rewarded with a 1-0 win after 18-year-old Jordan Ball headed home seven minutes from time to dump the holders out at the Keepmoat Stadium.
Wright said: "It was a disappointing goal to concede because we've played well and defended well. It's always going to be disappointing to go out of a competition you won last year."
He added: "If you switch off for a second, especially when you play teams from a higher league then you're going to get punished and it's frustrating that was the case.
"I thought we coped quite well with the possession Doncaster had - Richard O'Donnell didn't have many real saves to make and we had some really good chances on the break, particularly Craig Westcarr.
Meanwhile, Rovers boss Dean Saunders heaped praise on teenage striker Ball as his first touch in senior football booked Doncaster a place in the quarter-final. Ball - recalled from a loan at Northern League Division One side Belper - came off the bench to head home a David Cotterill corner and secure the win.
"It's basic with Jordan right now - he works hard and he scores," Saunders said. "He's got the right attitude, the work-rate and the basics you need to be a footballer. You either know where the net is or you don't and he headed it in like he's been doing it for years."
Saunders added: "He's scored eight goals in 10 games at Belper which has been great for him and that goal will have done him the world of good.
"It's great when a substitute comes on and wins a game like that for you. You need a bit of luck as a manager.
"That's probably the best we've played this season. The possession stats must be ridiculous because we had the ball all night."