The new inductees were missing Peter Gabriel, the theatrical lead singer whose departure was the dividing line between the band's two styles.
Former bandmate Mike Rutherford said Gabriel wanted to send his apologies for missing the event.
"He has a very legitimate and genuine excuse," Rutherford said. "He's actually starting a tour."
Anastasio recalled buying Genesis albums as a teenager. He called the band "rebellious, restless and constantly striving for something more."
"Every musical rule and boundary was questioned and broken," he said. "It's impossible to overstate what impact this band and musical philosophy had on me as a young musician. I'm forever in their debt."