Rodgers watched the Liverpool hand his Leicester City side a 4-0 thrashing to open up a 13-point lead on the Boxing Day.
Leicester, who are still in second place, were made to look inferior at the King Power Stadium.
Firmino opened scoring for the Reds in the 31st minute followed by James Milner’s penalty following Caglar Soyuncu’s handball.
It was Liverpool’s 17th league win from 18 matches this season wrapped up with Firmino’s second and Trent Alexander-Arnold’s strike.
Former Liverpool boss Rodgers, whose side were also beaten 3-1 at third-placed Manchester City on Saturday, said, “The last two games have been great benchmarks for us.
“Because of how well we’ve done, we’ve been catapulted into this title race, but then you’ve seen in the last couple of games, the quality of the opposition we’ve played, and Liverpool were absolutely terrific.
“They are going to be very, very hard to stop. There’s no doubt. They’re a fantastic team, with confidence high. They’ve become winners now, and haven’t lost many games now over an 18-month period.
“They’ve enough players, enough experience and enough quality to stay focused and get the job done.”
