Billups, who was an on-set guest on ESPN's "First Take," was reacting to commentary on the program that Griffin is perceived as "soft" around the league.
"I don't agree that Blake Griffin is soft. But what I will say about Blake is that he's maybe too nice of a guy," Billups said. "Because there's been times in games where people take shots at Blake. And I tell him if that's me, you're going to have to take this two- or three-game suspension, and I'm going to punish somebody.
"That's just how I'm built. Blake is not really built like that. He's ... too soft of a guy inside for him to be like, 'All right, I'm just going to hurt somebody.' He just won't do it. I wish he would, and I think that people would look at him a lot different if he did that. But he's just not that kind of person."
Billups said "there's nobody that works harder" than Griffin, but the three-time All-Star would benefit if the Clippers were able to add "a veteran down low to help him ... to push him along a little faster."
As for his own career, the 36-year-old Billups, who will be an unrestricted free agent this offseason, said he wants to play "a couple more years."
A ruptured Achilles tendon limited him to 20 games in the 2011-12 season. He played in just 22 games this season as he came back from the Achilles injury and dealt with various other injuries, but he said Thursday, "I feel like I'm back healthy again."
Billups, who was chosen Sunday as the first winner of the NBA's Twyman-Stokes Teammate of the Year Award, said he enjoyed his time with the Clippers but is monitoring the team's coaching situation after the dismissal of coach Vinny Del Negro before making any decisions.
"I'm watching with an eagle eye to see what happens. But we got good talent there. We'll just have to see what happens," he said.
Information from The Associated Press was used in this report.