Luis Suarez's fifth-minute opener and Jordan Henderson's second-half strike put Liverpool 2-0 ahead, only for the Gunners to suddenly click into gear and level thanks to Olivier Giroud and Theo Walcott.
"There is an initial disappointment when you are 2-0 up but we knew Arsenal were going to have a spell," Rodgers said.
"We could have had a few more goals but my overriding emotion is one of pride. Sunday was more my fault than theirs. I am a great believer in young players and I put a lot of trust in them.
"The problem is when I put them in and I don't have some of our big players, it's difficult.
"But I never had second thoughts about getting a reaction because these players have been brilliant."
- Sports & Recreation
- Olivier Giroud
- Jordan Henderson