The 18 year old made his first appearance for the first team when Kenny Dalglish handed him the right-back berth against Man City. Flanagan settled in immediately and impressed Carragher.
"He was outstanding. I'm delighted for him and I think it gives the whole club a lift when you see a local lad come through - the supporters love it," said the vice-captain.
"I think at the Academy it gives all of them a lift. The young lads at the Academy, it shows them it can be done.
"There's a bit of competition now between him and Kelly for the local lads. It's great for everyone really that you've got two local lads like that coming through.
"To be honest there's a few more down there so it's up to them lads to take their chance. Flanno's done that, but I'm pretty confident that there are more down there."