Visiting goalkeeper Dean Bouzanis was still lining up the defensive wall when Rovers winger David Cotterill curled a quickly-taken 20-yard effort past a posse of startled defenders and into the back of the net.
Dickov said: "It was a ridiculous decision by the referee to allow the free kick to be taken like that. Usually they stand over the ball before blowing the whistle for it to be taken.
"Our keeper was still lining up the wall and then suddenly the ball is in the back of the net. I'd like to ask the referee what exactly happened but apparently I need a personal invitation to speak to him."
Dickov was also unhappy about the sending-off of Bouzanis along with Doncaster striker Iain Hume in the closing stages.
Bouzanis pushed Hume following a foul by the Rovers striker on team-mate Connor Brown and Dickov added: "I would like to know why our man was given a straight red card while Hume was shown two yellows."