Chances were few and far between in the first half but Emmanuel Ledesma went close for the visitors after the break and Chris Brown missed the best chance of the match for Doncaster from close range on the hour mark.
Brown had a volley cleared off the line in stoppage time as the visitors' luck held.
Dickov said: "I thought we had the better of it. It was a scrappy match and it was hard to get the ball down and play because of the conditions.
"Middlesbrough are a good team and we knew they would be dangerous on the break but I thought we posed more of a threat overall."
Rovers skipper Richie Wellens was booked for a crude challenge and will miss the next two games as much-improved Doncaster try to extend their four-match unbeaten run.
Dickov added: "It's a blow to lose Richie but we didn't expect him to go through the next few games without a caution and it's a chance for someone else to come in and make their mark.
"I've said all along when we got our injured players fit we would be much more competitive and, with the signings we've made, we are a match for anyone when we are at our best.
"We've kept a few clean sheets in the last four games and we've got some important matches coming up so it's vital we keep the run going."