The Reds had three points firmly in their grasp at the Emirates Stadium after going 2-0 up inside the opening hour thanks to goals from Luis Suarez and Jordan Henderson.
However, Olivier Giroud pulled one back for Arsenal in the 65th minute and just two minutes later, Theo Walcott netted what proved to be the equaliser to earn the hosts a share of the spoils.
But although they ultimately failed to pick up a much-needed win, Rodgers was pleased with the way his players responded after last weekend's embarassing FA Cup fourth round exit at the hands of Oldham.
"There is an initial disappointment when you are 2-0 up but we knew Arsenal were going to have a spell," he 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."
Liverpool have been active so far in the January transfer window, signing Daniel Sturridge early in the month and Philippe Coutinho on Wednesday.
Tom Ince was also on their radar, but manager Brendan Rodgers does not expect the Blackpool winger to arrive before Thursday night's deadline, although he is not ruling a move out forever.
"I think it will be difficult now. We could still do the deal but it looks like one that is a bit too complicated at this stage," he said.
"It's about affordability as well. If Tom stays at Blackpool it doesn't mean he won't join Liverpool at a later stage."