On an evening when a number of second-tier sides were undone by lower-ranked opposition, Bongani Khumalo's 89th-minute header earned Rovers a 1-0 first-round win over League Two side Rochdale on a low-key night at the Keepmoat Stadium.
"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," Dickov said.
"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 so you have to give our boys credit for doing what they have done."
After an unflattering 3-1 defeat to Blackpool on the opening day of the Championship campaign, Doncaster were intent on attacking and created the clearer chances, twice hitting the crossbar through Chris Brown and James Coppinger.
Dickov added: "We kept a clean sheet, got the result and are in the hat for the next round. 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."