The result left fourth-placed Liverpool eight points off leaders Arsenal and their hopes of a title challenge appear to be receding although Rodgers was looking at the positives.
"We weren't great, but it was going to be very important we got something from the game. We've shown yet again great character to come back," he told reporters.
"It was a good point. I don't think we were anywhere near our level in the first half and I think you have to give credit to Aston Villa for that because they started very, very well.
"Their front two were a real threat for us and tactically we had to do something in the game to change it, to try and change the momentum.
"But have a look at the last week - Stoke away and Aston Villa at home. In the same games last season, we got no points from them. This time we've taken four out of the six."
Liverpool are awaiting news on Brazilian midfielder Lucas Leiva who came on as a second-half substitute but then left the field with a knee injury.
"He clashed knees with an opponent, so we'll just see how he is," Rodgers was quoted as saying on the Liverpool website (www.liverpoolfc.com).
"He just felt a little click in his knee. Hopefully it's not too serious. We'll not know for the next 24 to 48 hours."
Liverpool's next league action is on January 28 when they face Everton at home in the Merseyside derby.
(Reporting by Martyn Herman; Editing by Ken Ferris)
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