"You can't crown yourself as anything in this league," Revis told USA Today Sports. "You've got to earn it."
Revis widely had been considered the league's top cornerback in recent years. But he suffered a season-ending injury while playing for the New York Jets last year.
As Revis was rehabbing and before being traded to the Buccaneers, he and Sherman had a public battle for supremacy on Twitter.
"He needs to quit attaching his career to my career," Revis said. "A lot of people need to have respect for this game. I'm not just talking about him. Respect what people have done to pave the way. Deion [Sanders] paved the way. Rod Woodson paved the way. Darrell Green. Mel Blount. Champ Bailey. Charles Woodson. Yeah, we're the next group, but you don't need to be getting into it with me.
"At the end of the day, this is a fraternity. We're all in this together, competing. But you don't have to shoot nobody else down."
The Buccaneers play the Seahawks on Nov. 3 in Seattle.