President Trump told donors he is unhappy with the Federal Reserve’s recent moves to raise interest rates and raised doubts about the man he placed in charge of the institution, Jerome Powell, people in attendance at a fundraising event said.

Mr. Trump said his advisers told him last year Mr. Powell would support “cheap money” as the Fed’s chairman, and then Mr. Powell surprised him by embracing rate increases, which the president fears will cool off the fast-growing economy.

“That...