The Merseysiders twice fell behind at Craven Cottage on Wednesday as Kolo Toure sliced past his own goalkeeper before Kieran Richardson made the most of Martin Skrtel's deflection to score from close range.
On both occasions, though, Liverpool pulled level. First, Gerrard's exquisite pass was received by Daniel Sturridge, who kept his cool with a neat finish, before Philippe Coutinho cut inside to strike home from 20 yards.
It looked like Liverpool would be frustrated in its efforts to find a winner until Sturridge was chopped down by Sascha Riether in the last minute, and Gerrard held his nerve to convert the penalty.
"Steven is peerless in many aspects of football," Rodgers said. "His performance again was [brilliant]. His pass for the first goal, that penetration he has that he's shown all his life and then the composure at the end.
"It's no coincidence, he studies the goalkeepers and what side they dive. The professionalism he's showing at this stage of his career is still there. There's no more ideal person than Steven Gerrard when you have a penalty in the last couple of minutes in games, he stuck it away brilliantly."
Rodgers is also unconcerned by Luis Suarez's current run of three games without a goal and insists the Uruguayan continues to influence in other areas.
“Luis is a world-class player, but I'm building something here that isn't reliant upon one player,” said Rodgers. “Other players have scored goals when Luis wasn't in the team, or Daniel wasn't in the team. You don't score the number of goals we do when you're reliant upon one player.
“Would Luis want the golden boot or be in the Champions League? He'd want to be in the Champions League. He's such a selfless player, working wide and pressing all the time. The team is the most important thing.”
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