MILFORD, N.H. — If people thought that his second-place finish in Iowa had discouraged Donald J. Trump or distracted him from his goal of winning the Republican presidential nomination, Mr. Trump made it clear Tuesday night that they were dead wrong.

In his first public appearance since he placed second to Senator Ted Cruz of Texas in Monday’s Republican caucuses, Mr. Trump told reporters and later a rally of 5,000 people here that he had started out last year given no chance in Iowa and ended up almost winning.

He also predicted he would do better in New Hampshire because “it suits me better.” He did not specify why, but the state has far fewer religious voters than Iowa. He did say New Hampshire has “a normal voting process,” meaning a primary, which does not require the intense organization that Iowa’s caucuses do.