Two own goals, and a frantic finish which saw four goals scored in the last eight minutes, gave the Reds a less-than-convincing victory over their bottom-placed hosts.
And Rodgers was the first to admit his side had been very fortunate to walk away for Loftus Road with maximum points.
“They certainly didn’t deserve to lose, QPR,” he told Sky Sports. “We were very, very lucky to get the win.
“We showed tremendous character and were a little bit better in the second half, but QPR definitely deserved something.
“We put players on to play a game, which is a technical game. The first half, we didn’t pass the ball, we had no rhythm in our game, movement was too slow, no speed in the game.”
Rodgers reserved special praise for Liverpool’s only goal-scorer of the day, Philippe Coutinho, as well as England international Raheem Sterling.
“Coutinho coming on gives us that technical lift in the game and we then started to create that bit more,” he said.
“I thought Raheem Sterling was outstanding today in his running and desire. It was really quick thinking for the first goal and he broke away on the other one.
“Overall we were fortunate, but it’s a long season and you’re going to not play well in games. You hope to get points and today we got three points, but QPR were unfortunate.”
Liverpool take on Hull City, who drew 2-2 with Arsenal on the weekend, in their next fixture on Saturday afternoon.