A second-half Michu equaliser denied the visitors all three points, ending their winning run as their clean sheet record also came to an end despite goals from Daniel Sturridge and debutant Victor Moses.
However, after going behind to a Jonjo Shelvey goal two minutes in, Rodgers was pleased with how his side battled back.
"Tonight a point is good for us," he told Sky Sports.
"The first 65 minutes of the game we were very good with and without the ball. We showed great character to come from behind so early on in the game and [Philippe] Coutinho going off probably disrupted the flow of our game.
"It was two teams that were offensive and wanted to win the game. We came here to maintain our winning streak but it's important that when you can't win, you don't lose."
Shelvey had an eventful match against his former employers, with two poor passes allowing Liverpool to lead at the break.
However, Rodgers insisted that the 21-year-old will learn from the experience and become a better player for it.
"Jonjo is a very very good young player and he showed that in his first goal by getting in the box and putting it [his goal] away well," Rodgers continued.
"He needs nights like this. I didn't want him to go and he probably didn't want to go but he knew it was in his best interests as a young footballer to go and play.
"He got caught out a couple of times which obviously led to our goals but he'll be better for the experience and he'll develop into a very good player."
The win edges Liverpool back into top spot, despite dropping their first points of the season.
With Luis Suarez set to return from his 10-match suspension for biting Branislav Ivanovic last season, Rodgers believes that the Urugyuan will provide a boost for his side.
"We've still got one of the best strikers in the world to come back into our team," Rodgers continued, adding that Coutinho was "very sore" after he was forced off following a challenge from Ashley Williams in the second half.