The Liverpudlian heavyweight was stopped in the fifth round of their rematch at the Liverpool Echo Arena.
Price's promoter, Maloney, feels that Price should now target fights at a lower level after his second defeat in as many bouts with the American.
"We've dropped out of the Premier League and we need to target fights at domestic and European level," Maloney told BoxNation.
"We are all in shock and we will have to sit down and talk about what we do next. If David wants to go on, I'll stay loyal. If he doesn't, I may call it a day."
Price's unbeaten record was taken when he was beaten by Thompson back in February.