Mr. Bloomberg’s debate performance on Wednesday proved so lackluster that both supporters and rivals counted themselves taken aback, leaving his campaign more rattled than at any point since he entered the race. While Mr. Bloomberg sought to project a steely calm on Thursday during a swing through Utah, he and his team have been left to explain away a comedown that exposed some of his gravest liabilities.

Howard Wolfson, one of Mr. Bloomberg’s closest advisers, on Thursday shouldered the blame for the outcome of the debate.

“I led the debate prep and I accept the responsibility for inadequately preparing him,” Mr. Wolfson said.

Several people close to the Bloomberg campaign, who spoke on the condition of anonymity to discuss private concerns, said that the former New York mayor’s advisers had quietly acknowledged that Mr. Bloomberg would have to take a wholly different approach to the next debate, in South Carolina on Tuesday night.