Allen became Rodgers' second Liverpool signing when he joined from Swansea in 2012.
"He came into a club of this magnitude - to sustain how he started the season for a whole season was always going to be difficult," said Rodgers.
"He was outstanding in that opening period. Like all players, they go through different stages of form and confidence. I've worked closely with Joe for a couple of years so I know his talents and qualities.
"I know he will end up being a super player for Liverpool. We brought him here for the now but going forward as well.
"He's a wonderful technician, tactically strong but can physically cope with the battle. It has been difficult for him because of his shoulder; it was under wraps for a long time and he didn't want that to be thrown out there.
"His body work is vital in his game and it got to a point where it wasn't doing him any favours. So it was best to get that done, get the surgery completed and it means we get a player back in pre-season fully fit.
"The first three months of the season he was Player of the Month so the Liverpool supporters saw in that opening period that he has qualities. He always wants the football and it takes courage to be that type of player and he showed that by the bucketload.
"Of course you have up and down spells but I've got every faith in him. He's a good boy and a very humble player who always wants to get better.
"He now knows what it takes to be a Liverpool player and if he can continue to play how he did at the beginning of the season, and he's fully fit, he'll be a great asset for us."