The Scot equalised for Leicester on 66 minutes to cancel out Mark Yeates's first half strike for Colchester.
In the absence of the suspended Steve Howard, Barry Hayles was handed his first League start of the season while Lloyd Dyer made way for Max-Alain Gradel on the wing.
For Colchester Neal Trotman made his debut after joining on loan from Preston.
The first chance fell to City on 12 minutes when Andy King half-volleyed Matty Oakley's corner just over.
Colchester had to wait until the 20th minute for their first meaningful attempt when from the tightest of angles Yeates shot wide of Tony Warner's goal.
Yeates did much better on 23 minutes, however, when he curled a right-foot free-kick from 22 yards over the City wall and into the far corner of Warner's net.
Dyer came on for the injured Tom Cleverley on 34 minutes and almost immediately supplied a dangerous cross which Michael Morrison headed narrowly wide.
There was more urgency to City's play after the restart with Oakley placing a cross just out of the reach of Hayles before Matt Fryatt turned on a Dyer cross and fired just over from eight yards.
The Foxes then had a scare on 62 minutes when an unmarked Karl Hawley headed a good chance just wide.
Gradel made way for Dickov on 66 minutes with the Scot levelling after just 30 seconds of entering the fray.
Oakley scooped back in a half-cleared corner which Mark Cousins could only parry to the feet of Dickov who fired home from ten yards.
Warner kept City level with two tremendous saves, first when he blocked a Clive Platt header at point blank range and then when he stood his ground to beat away a shot from Yeates after the Colchester winger had outstripped the City rearguard.
Fryatt had a chance to steal it for City ten minutes from the end when he seized on a back pass but he was disappointed to blast an angled drive over the bar.
Dyer then squandered a clear chance to win it for the home side three minutes from the end when he latched onto a Fryatt pass only to be foiled by a brave save from the keeper.