Moss, a former teammate of Griffin, spoke Monday in an interview with 106.7 The Fan.
Shanahan was fired in 2013 after four seasons with the Redskins. He posted a 24-40 record.
Griffin was the No. 2 overall pick by the Redskins in the 2012 NFL Draft.
"You can't do that," Moss said on the show, regarding Griffin gloating about Shanahan's dismissal. "One thing I'll just share with you: God don't like ugly. So the little credit that he did take for saying that, 'Hey, they didn't like what I was doing,' or 'they benched me and not allowing me to play,' that's what happens."
"So 2014 comes, and Jay Gruden comes in, and he don't care. We see that now. He doesn't care. He doesn't care what he says about you, he doesn't care what he says at you."
"And he rips RG every chance he gets, like every meeting, and we're sitting there looking like, 'Yeah. You know what? You were just so happy that Mike and Kyle and them is gone, but now you're getting your behind ripped every day, because you're not playing the kind of football that we need to play for us to be successful.'"
"So it comes back and bites you in your behind. Because now you see this guy is at home. And, to be honest with you, I give it to you raw. I don't know no other way to give it to you - raw and uncut, I always say that."
Griffin made the Pro Bowl in 2012 but posted a 5-15 record as a starer while throwing 20 touchdowns and 18 interceptions in 2013 and 2014 for the Redskins. He joined the Cleveland Browns on a two-year contract in 2016 but was released after one season.
Moss was asked to clarify if he meant that Griffin was gloating about Shanahan being fired. He confirmed that sentiment.
"Yeah, you can't do that," Moss said. "You can't do that. I don't want to ever see somebody ... I mean, you see guys coming in and out of those doors - as players, as coaches, as members of the team, however, trainers, staff members, period - and you don't like to see them go, because you know that's taking something off their plate. So, I live by that. God don't like ugly, man, so try not to be in those shoes, to be the guy to reap off of someone's downfall."
The former Heisman Trophy winner went on the defensive after the call out from Moss.
"No subtweeting needed," Griffin tweeted Tuesday morning. "Santana Moss, I treat you like a brother & have always had your back. To openly lie about me is a betrayal."
No subtweeting needed— Robert Griffin III (@RGIII) September 19, 2017
Santana Moss, I treat you like a brother & have always had your back. To openly lie about me is a betrayal.....
"Been lied on a lot over the years."
"Put in an impossible situation w/ a coach who never wanted me," Griffin added. "Made players like Santana Moss a believer through hard work, film study...showing up early, leaving late, putting in the extra hours, staying after practice & getting extra work in. We won the division that year"
"Next year coach wants out, says he wants out, says he never wanted me as his QB & I GET BLAMED? C'mon man. I have been the good soldier," Griffin said.
"Some so desperately want me to fit this negative narrative that has been pushed about me. But I don't fit it. Never have. Never will," Griffin said.
Next year coach wants out, says he wants out, says he never wanted me as his QB & I GET BLAMED? C'mon man. I have been the good soldier.— Robert Griffin III (@RGIII) September 19, 2017
"Proved it in Cleveland. Voted Captain. Came back to play for my teammates just to help us win 1 game. With a broken shoulder. Stop the lies."
Griffin posted a 72.5 quarterback rating in four starts in Cleveland last year. He was linked to the Seattle Seahawks, Baltimore Ravens and Los Angeles Chargers this offseason but remains a free agent.