"I don't want America to think all Brits are like David Price," Fury told the Manchester Evening News. "I can't let Thompson get away with that - I will have to take him out for Price.
"I'm gutted for Price as a fellow boxer. He's put in all the hard work and fallen at one of the last hurdles. It could happen to anyone and it's just happened to him. He might come back. He's always got a puncher's chance. He's got a big punch but often the big punchers can't take them back.
"Cunningham is a lot harder fight. After him I will take Thompson and show Price how to deal with a granddad. I guarantee it won't last longer than three rounds. I will blitz him."
Thompson called out Fury after defeating Price, dubbing him a "sissy". The pair are expected to meet in the ring sometime after Fury's IBF title eliminator with Steve Cunningham in New York in April.