The former boss believes the midfielder still had a lot to offer the club despite his age.
The former England captain has brought an end to his life-long association with the club by agreeing a deal to join MLS side LA Galaxy back in January.
The midfielder recently celebrated his 35th birthday, and endured a disappointing final season with his side as manager Brendan Rodgers elected to leave him out for most of the big games.
Evans though, believes it was a mistake to allow the player to leave as he still has a lot to offer.
“I think they should have tried hard to keep Steven,” he said.
“People say he is getting older but for me he still has a lot to offer. I think Liverpool have to forget about the potential in many ways and they have to get players who know they are going to do the job.”
There were also questions about the recruitment policy at the club with several players arriving but failing to impress, with Mario Balotelli chief among them.
One positive though was the emergence of youngster Jordon Ibe, and Evans is hopeful the youth mixed with experienced players will leave the club with a strong squad next season.
“We have a great academy with a lot of lads with good potential coming through the academy,” he added.
"Jordon Ibe and people like that have signed a contract so hopefully with a mixture of some experience and some younger kids we’ll have a better squad and at least a better attacking option.”