The Reds boss felt his side could have been awarded two spot-kicks in a keenly-contested tie at Anfield in which the Sky Bet Championship side defended tigerishly to secure a replay at Ewood Park.
Rodgers told BT Sport: "They defended very, very well and when you have that many bodies behind the ball - and they were very brave, got blocks in - and I thought we should have had a penalty.
"In games like this sometimes in that opening 20 minutes, if you can get the first goal, it opens the game up.
The Emirates FA Cup
Blackburn take Liverpool to quarter-final replay
"Adam Lallana's one looked a clear penalty. The defender is recovering back in, but he's on the wrong side and he can't get to the ball, so for me, that was a penalty.
"You could argue when [Rudy] Gestede handballs it off the header from the free-kick, we could have had another penalty, and sometimes you need that little bit of luck.
"They have got some good players - Gestede gives you a problem up front - but I thought in the main, we dealt with that really, really well.
"I thought maybe the sharpness was just missing from our game and that wee bit of incision. But credit to the players, they kept a clean sheet and the objective was to be in the hat for the next round by the end of the evening, and that's what we are in."
Rovers skipper Matthew Kilgallon was quick to insist the home side did not deserve a penalty for his challenge on dangerman Daniel Sturridge.
He said: "No, no, no, no. You have got to be tight to him. You give him a yard and he's got that shot with no back-lift. Maybe when I did give him that yard, he has got the shot off.
"You have got to be tight to these players and that's what I was."
Things might have been worse for Liverpool had it not been for a fine 49th-minute save by keeper Simon Mignolet to claw Alex Baptiste's header out of the top corner.
Baptiste said: "I was free at the corner. They mark zonally and I thought it was in, to be honest."