Flanagan fired in a fine finish for his first Liverpool goal as the Reds thumped Tottenham 5-0 at White Hart Lane on Sunday, a result which brought about the sacking of Spurs boss Andre Villas-Boas.
Captain and lynchpin Luis Suarez scored twice and had a hand in Liverpool's three other goals.
The Uruguay forward and Jordan Henderson drew lavish praise from their manager, but Rodgers also found time to pay tribute to 20-year-old defender Flanagan.
Rodgers had looked to send the homegrown youngster on loan for experience, but admitted he changed his mind after Flanagan's eye-catching performance in the 3-3 derby draw with Everton last month.
Rodgers said: "Only one club has come in for him on loan, a club in League One.
"He's a terrific boy that has played for the under-21s, in practice games with about two people watching.
"And whoever he's up against, he doesn't change. I thought when he came in for a few games this was a kid that can handle it.
"And since he came in and played in the derby, where he was man of the match against Everton, he's been fantastic.
"His confidence has grown and grown over time.
"A young player like that, probably a couple of years ago, might not have had a chance.
"Or maybe someone comes in, does well for a few games then drifts away.
"So I've said to him, 'just play every game as if you haven't cracked it, go out and be the best you can be', and that's what he's done.
"His goal was a brilliant finish. I'm delighted for him, he's a real good boy and you can see how much it means for him and the supporters."
Liverpool's victory at Spurs pushed them up to second in the Premier League table, but Rodgers was quick to play down any talk of a title tilt this term.
He said: "We're not even thinking about that to be honest. We're working on our style of football going forward.
"You can be looking to finish fourth, or third or second, but eventually you want to be winning the league.
"The year before I came it was eighth, then last season we finished seventh.
"But realistically we just have to keep fighting. You look at the depths of some of the squads.
"If we can keep continuing to improve our football, let's just see where that takes us."