Bradshaw, who won four Super Bowls as the Steelers' quarterback from 1970 to 1983, appeared as a guest Friday on Fox Sports 1's "Speak For Yourself."
"I don't think he's a great coach at all," Bradshaw said of Tomlin. "He's a nice coach. To me, I've said this, he's really a great cheerleader guy. I don't know what he does. I don't think he is a great coach at all. His name never even pops in my mind when we think about great coaches in the NFL."
Bradshaw said he considered Tomlin's predecessor, Bill Cowher, to be a great coach. In his 15 years as Steelers head coach, Cowher was 149-90-1 (.623) from 1992-2006, with 10 playoff appearances, two AFC championships and one Super Bowl title. He had three seasons under .500.
Bradhaw's coach, Chuck Noll, had 193 career wins from 1969-1991.
As a comparison, Tomlin has never had a losing record and his overall mark is 101-57 (.639) in 10 seasons with the Steelers, including winning Super Bowl XLIII on Feb. 1, 2009. He is one of eight head coaches in NFL history to win at least 100 games in the first 10 years on the job.
Steelers director of communications Burt Lauten weighed in Friday night on Twitter in defense of Tomlin.
"Friendly reminder: #Steelers HC Mike Tomlin won SB XLIII (2 apps), won AFC North 4x, is 101-57 (.639) & fastest in team history to 100 wins," Lauten tweeted.
This year's Steelers (9-5) have won five straight games and can clinch the AFC North with a win over the Baltimore Ravens (8-6) on Christmas Day at Heinz Field, which would put Tomlin's team in the playoffs for the seventh time in his 10 seasons.