Goals from Jordy Hiwula and Luke Thomas lifted Mark Robins’s side into the play-off positions and dropped Doncaster, without a win in three, down into eighth.
Joe Wright smashed a goal back midway through the second period and much-improved Rovers almost grabbed a point late on when John Marquis saw his shot cleared off the line.
“We need to make sure the next game we play we get the team right,” said McCann.
“Today I didn’t pick the right team. That’s a fact and that’s the reason why we didn’t play well in the first half.
“In the second half when we made the changes and we changed the shape a little bit we looked more of a threat. I take responsibility.”
Suspended duo Andy Butler and Niall Mason were replaced by Tom Anderson and Ali Crawford, with Matty Blair dropping back to right-back.
Rovers switched from 4-3-3 to a midfield diamond after the interval andMcCann made a double change just before the hour mark when Jermaine Anderson and Paul Taylor replaced Crawford and Mallik Wilks.
Coventry took the lead after 20 minutes when Hiwula rifled in an unstoppable volley.
The Sky Blues doubled their advantage after 41 minutes when Thomas unleashed a spectacular effort in off the post.
Coventry City: Burge, Sterling, Willis, Davies, Brown, Thomas, Bayliss (Kelly 64), Doyle, Hiwula (Ogogo 81), Chaplin (Jones 71), Clarke-Harris. Unused substitutes: O’Brien, Hyam, Bakayoko, Thompson.
Doncaster Rovers: Marosi, Blair, Wright, T Anderson, Andrew, Crawford (J Anderson 57), Whiteman, Kane, Coppinger, Marquis, Wilks (Taylor 58). Unused substitutes: Lawlor, May, Longbottom, Amos, Horton.
Referee: C Boyeson (E Yorkshire).