The England international - signed from Southampton during the close-season - has started the Anfield club's last two Premier League matches, playing the full 90 minutes in a 1-1 Merseyside derby draw with Everton on Saturday.
And Rodgers, who also picked Lallana for the midweek League Cup clash with Middlesbrough, believes the 26-year-old is improving quickly.
"I thought he was outstanding," said Rodgers. "To come into his first derby game and play with that quality and intensity [was impressive].
"And he played the whole game in midweek against Middlesbrough. To deliver that performance was great because it shows me he's getting fitter and fitter now with each game.
"I thought his performance was outstanding."
Liverpool face Basel in the UEFA Champions League on Wednesday.
