The mid-table SkyBet Championship side certainly had the better of the first half but Rodgers felt Matt Kilgallon should have been penalised for a foul on Adam Lallana.
There was a second incident after the break when substitute Mario Balotelli appeared to have his shirt pulled inside the area, but ultimately Rodgers had to concede his side were not at their incisive best.
"The last three months we have been in outstanding form and the physical and mental energy we put into games is at such a high level," he said.
"Today we just lacked that bit of sharpness physically. You want to try and grind your way through the game. We did that.
"There is a physical energy in how we play and it is natural sometimes there will be a little bit of cost and that affected the speed of our play.
"Give Blackburn credit. The defended well in a low block, really well, and put their bodies on the line and made it really difficult for us
"I definitely thought we should have had one penalty. Adam Lallana got his body between the man and the ball and as he went to shoot he was knocked over.
"I thought that was a clear penalty. The others were debatable.
"We probably needed that bit of luck to get the game opened up."
Liverpool struggled to get going after an eight-minute injury break when Martin Skrtel fell awkwardly and was eventually carried off on a stretcher wearing a neck brace.
"He is fine but he will go to the local hospital to make sure
If he had his choice he wouldn't but we have to follow procedure," added the Reds boss, who said captain Steven Gerrard would be fit for the trip to Swansea a week on Monday after missing seven matches with a hamstring injury.
"He was fine, up walking and talking after the game but as a precaution we need to make sure he is okay."
Source: PA