Jones was suspended and stripped of his light heavyweight title after he was implicated in a hit-and-run accident that saw a pregnant woman suffer a fractured arm and wrist.
"You don't kick a guy when he's down. It was obviously disappointing. All the stuff Jon gets into is disappointing. He can't seem to get out of his own way," Cormier told UFC Tonight's Michael Bisping and Kenny Florian on Tuesday.
Following Jones's suspension, Cormier has been confirmed as 'Bones' replacement as the headline act at UFC 187 on May 23, where he will take on Anthony Johnson for the now-vacant light heavyweight title.
"'Rumble' Johnson is a fantastic fighter. He has tremendous power and has a confidence about himself, now," Cormier added.
"At his core he is a guy that got submitted by [welterweight] Josh Koscheck, a guy that tapped out before [middleweight] Vitor Belfort had a choke on him. At the core, he is who he is. I just have to find that."
Cormier, though, is the first to admit that the winner of his fight with Johnson wouldn't be the true champion since Jones didn't actually lose his title.
"I'm a realist," he added.
"Jon was the champion. He beat himself. Nobody beat him. I didn't get the job done Jan. 3. It is a tough hill for me to climb. It will not be easy. Jon did this to himself; the belt is not his anymore. So, this is the real championship.
"Just get it together. Get it together, man," he added when asked what he would say to Jones should he have the opportunity.
"I'll be waiting on the other side with my championship and he can actually challenge me for it."