Franck Moussa volleyed home Ciry's opener in the third minute and Rovers squandered chances before on-loan Nottingham Forest striker David McGoldrick added the second.
McGoldrick missed a good chance to score again before he added the third from close range in the 58th minute.
Rovers tried hard to fight back and Chris Brown pulled one back with a header in the 76th minute before Adam Barton wrapped up the points for Coventry in fine style with a superb strike in the last minute.
Saunders said: "It was a disastrous result for us.
"Conceding four goals is totally unlike us and I can only put it down to a bad day at the office.
"We didn't defend well at all and that's really been our strength this season.
"It looks like a heavy defeat but I pushed players forward and that left us a bit vulnerable and they took advantage by scoring the third and fourth, but really it was the first two goals that did the damage.
"We were joint-top and we've got a slap in the face. Now we've got to bounce back."