Rose announced last week that he would skip Saturday's gala because he didn't feel "wanted or respected" by his former bandmates. The 'Welcome To The Jungle' singer also requested not to be inducted "in absentia".
Guns N' Roses' Hall of Fame induction went on without the frontman in Cleveland, with Rose's name apparently drawing boos when he was mentioned during the ceremony.
Adler, who drummed for Guns N' Roses from 1985 to 1990, spoke of Rose's absence with Rolling Stone following the Rock and Roll Hall of Fame concert.
"All I have to say is I love Axl very much and I was blessed that... he was a part of my life," Adler noted.
The drummer went on to express hopes that Guns N' Roses' induction into the Rock and Roll Hall of Fame will pave the wave for many of his other favourite bands.
"It's such an honour to be inducted into the Hall of Fame, but then I found out that KISS isn't in here, and then I found out the other day that Rush isn't in there," Adler said.
"They've got to be inducted. If it wasn't for those bands and a couple other ones, there wouldn't be a Guns N' Roses."
Adler was joined at the induction ceremony by Guns N' Roses guitarist Slash, bassist Duff McKagan and fellow drummer Matt Sorum.
Those four joined with Alter Bridge's Myles Kennedy to perform two of Guns N' Roses' classic tracks, 'Sweet Child O' Mine' and 'Paradise City'.
Red Hot Chili Peppers, The Faces/The Small Faces, the Beastie Boys and Laura Nyro were also inducted into the Rock and Roll Hall of Fame in Cleveland on Saturday (April 14).
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Watch the former Guns N' Roses stars perform 'Sweet Child O' Mine' in the Rock and Roll Hall of Fame concert below: