Flanagan was played in an unfamiliar left-back role for his first ever Merseyside derby, and Rodgers feels that the youngster's contribution was outstanding.
"Jon Flanagan was immense," Rodgers is quoted as saying in The Mirror.
"A young kid from the city, given the chance to play in a derby game that will be on 'Sky Gold' in about 30 years' time, and given the chance because of his desire to put himself out there every day.
"He did brilliant, and that gives me something to think about. He needs to play football, but if he plays like he played against Everton, he's going to get football."
The Reds are currently second in the Premier League.