League Two Dale looked like taking the tie in extra-time until Khumalo headed home the winner in the 89th minute on a night when a number of Championship sides were humbled.
"The test for me is when I get into my office five minutes after the full-time whistle and see the other sides who have gone out," said Dickov.
"I know what it's like to be the underdog and have been in Rochdale's position before. I thought they were fantastic and came here with no fear.
"A lot of teams have slipped up tonight so you have to give our boys credit for doing what they have done."
Rovers were beaten 3-1 by Blackpool on the opening day of the Championship season but Doncaster showed more attacking intent against Rochdale, as they twice hit the bar through Chris Brown and James Coppinger.
"We kept a clean sheet, got the result and are in the hat for the next round," added Dickov.
"At the moment, when we look good, we're good, and when we're poor, we're poor. But the main thing for us is that we're in the hat.
"We are creating chances but when we are on top we need to put them away and sustain the pressure.
"We are playing in fits and starts at the moment but the longer we go, the better we will be."
Dickov's counterpart Keith Hill refused to speak to the media after the game.