Daniel Sturridge and Adam Lallana netted after half-time at Selhurst Park to secure progress into the sixth round.
Fraizer Campbell had given Palace a 15th-minute lead to stir memories of Liverpool's 3-1 Premier League defeat in London last November.
But Rodgers believes that loss helped to inspire an upturn in form among his squad, who have now lost only twice in 22 subsequent games.
"Earlier on in the season we weren't so good here at all but it was the making of the team really," he told BT Sport.
"It's obviously a difficult place to come. Alan [Pardew, Crystal Palace manager] has come in and done a great job here. It was always going to be tight and difficult.
"I thought we were very, very good after they scored the goal. We started a bit slow and weren't aggressive enough.
"I think we had 15 efforts on goal in the first half. I felt our three defenders needed to be more aggressive and go and attack the ball. We also needed to get in and around the second balls a wee bit more."
Reflecting back further on Liverpool's earlier humbling at Palace this term, Rodgers added: "We'd no pace, we'd no penetration in the team. Our performance level and results couldn't have got any worse.
"We needed to arrest the momentum that was going in a negative way and, following that, we got seven points out of nine.
"In that period it was about trying to do a system and a solution where we could get our intensity back and get our technical players on the field.
"From that period here in November we've been on a really, really good run."
