The Reds started with a 5-3-2 formation and fell behind as John Terry got away from Daniel Agger to head home, before the Blues captain was stretchered off following an accidental collision with Luis Suarez.
Rodgers changed to a four-man defence on the hour mark when Suso came on for Nuri Sahin and was rewarded when Suarez nodded home Jamie Carragher's flick-on from a corner with the home side sleeping.
He told Sky Sports: "I thought in the first half we were too tentative. Second half our attitude in the game was much better and we are better when we play fast football.
"Coming here is a very difficult place. I thought it was a great point for us. You have to give credit to the players, they were fantastic.
"Whatever system you have, it doesn't matter, it is about the application and the quality of the players."
Rodgers also hailed Carragher, adding: "He is phenomenal, it's an absolute pleasure to work with him. His preparation is first class, he is always preparing himself well.
"Today he was exceptional, he is a real model professional for a young player. With everything he has won and achieved he could easily come and knock on my door but he is old school, he respects authority."