Jamie Vardy hit the post just before the interval but City never landed a shot in the second half and Doncaster could have won by a wider margin had Chris Brown not fired a good chance over near the end.
Dickov said: "We came up against a top team and competed very well with and without the ball.
"It takes a lot of courage to have a go against teams like that but we've done it and been rewarded .
"We had a couple of regulars missing through injury and illness but I always like to talk about the squad and players that have come in and done their jobs well.
"There's a real togetherness throughout the club and the attitude of players not occupying first-team spots has been first-class.
"I didn't actually see the goal when the ball went in but I think we were due one after not getting our just desserts with some of our recent performances.
"People talk about passing the ball well and other things but you have to do the nitty-gritty as well and that's what we've done today."
Dickov added that he was trying to extend the loan of Manchester United striker Federico Macheda to the end of the year.