The Reds boss saw his side race into a three-goal lead by half-time courtesy of goals from Luis Suarez, Daniel Sturridge and a penalty from Steven Gerrard.
Palace improved after the break but Rodgers admits it is hard when you are so comfortable at half-time.
"It was an excellent first half and we got the three goals and could have had two more," Rodgers told Sky Sports.
"Some of our play in the attacking third was exceptional and we created a number of chances.
"Second half is always difficult when you are comfortable in a game, we wanted to go and push on in the second half and it didn't quite materialise and you have to give credit to Crystal Palace.
"I think Ian's side worked very hard in the second half and align that with some of our loose passing but overall it is three points and that is the aim and we are pleased with the result and hope to improve on our performance level."
Suarez's goal was full of commitment as he swept home after tripping in the box, and Rodgers was delighted with the Uruguayan who he says has a 'telepathic' understanding with Sturridge.
"It typifies the man, he gives 100 per cent and tripped over in the box and got himself to the ball and scooped it in," he said.
"I thought him and Daniel Sturridge were exceptional up there today and particularly in the first half and you could see the link-up play they have that telepathic idea of where they are and it is great to see and very encouraging.
"I believe top players are often on the same wave length and them two are."