The teenager, who made his Champions League debut in the win at Ajax, had been given a first senior Reds chance alongside Van Dijk in the Carabao Cup tie at Lincoln City last month.
"It's a nice story," said the Reds boss of Williams' European bow. “I saw it in his eyes after the game that he was pretty impressed by that occasion.
“He is a big talent, not only physically big but is a real talent. It is nice to have him around.
“He played last year in non-league, and that makes it special.
“As always in life, when something bad happens, when the dust settles you can see the opportunities again.
“It's all about doing the right things in the right moment. For Rhys it was his first Champions League minutes."
Klopp added: “With our situation, we have Nat Phillips here as well and Billy the kid and they are really around.
“Nat Phillips we thought would be transferred, but at the last second it didn't happen.
“These are solutions for us, and help us a lot. The boys are great, and it is a big opportunity for them."