Depp joined the rock legend on stage at London's 100 Club on Sunday night, playing guitar on several of the singer's most popular tracks including 'School's Out'.
Cooper said that he would be happy to perform with Depp again in the future, before comparing his musical skills to that of iconic Guns N' Roses guitarist Slash.
"I'd work with him again," Cooper told Bang! Showbiz, following the performance. "I mean the guy is a valid guitar player, we told him anytime he wants to come up and play, feel free.
"We've always given that kind of privilege to any great guitar player, like Brian May. He's in the same place as Brian May or Slash."
Cooper said that he loved watching the reaction of fans when 'Johnny D' took to the stage, as they slowly realised it was actually the Pirates of the Caribbean star on guitar.
Depp has previously played guitar on the Oasis track 'Fade In-Out' and is reportedly being courted by Liam Gallagher to star in his production company's biopic about The Beatles.
Cooper will begin his 'Halloween Night of Fear' tour in the UK this October.
Watch Johnny Depp join Alice Cooper on stage for a performance of 'I'm Eighteen' below: