Summer signing Albert Adomah continued his hot streak by bringing up five goals in three games with a well-taken brace before half-time.
Kei Kamara put the result beyond doubt midway through the second half before Daniel Ayala, who arrived on loan from Norwich on Tuesday, put the finishing touches to Boro's impressive victory.
Rovers enjoyed most of the possession in the first half but after being hit twice on the counter-attack, Dickov's defence went to pieces, leaving the Scot furious.
"Poor, really poor," was the former Oldham manager's frank assessment.
"For the first time since I've come here it's very hard to pick any positives out of it.
"We pride ourselves on our work-rate and desire without the ball and that was missing.
"I'll find out and put it right because I'm not standing for it. They had more energy than us, they had more desire than us and the result reflected that.
"They'll soon realise that I won't accept a performance like that."