The Blues captain John Terry put the home side ahead in the first half with a thumping header past Liverpool goalkeeper Brad Jones from Juan Mata’s corner.
Former Liverpool striker Fernando Torres had a chance to extend Chelsea’s lead after the interval, but the Spain international was denied by an alert Jones.
And Rodgers’ men rescued a point at Stamford Bridge when Jamie Carragher flicked Suso’s cross into the path of Suárez, who nodded home from close range.
“We were too tentative in the first half,” Rodgers told Sky Sports.
“In the second half our attitude was much better. We’re better when we play fast football and attack, and we could have gone on to win the game.
“It’s a terrific point for us because coming here is a difficult place. So for us, with the team we have at the current moment, it was a great point for us.”
Meanwhile, Carragher, who was starting his first Premier League game of the season, admitted Liverpool need to start turning draws into victories if they are to move up the table.
“Chelsea are playing well this season,” said Carragher.
“They have good attacking players in the final third. At half-time the manager said we were quite tentative.
“We were not willing to take the chance and in the second half we were more willing to get forward. It’s a great learning curve for the young players.
“It is a nice little run we have got going but we want to turn draws into wins. It is a good point but we have to kick on now and start getting some wins.”
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