Michael Cohen has disavowed responsibility for some of the crimes to which he has pleaded guilty, privately contending in a recent recorded phone call that he hadn’t evaded taxes and that a criminal charge related to his home-equity line of credit was “a lie.”

As he prepares to begin a three-year prison term on May 6, Mr. Cohen, President Trump’s former lawyer, expressed dismay during the conversation that after testifying for more than 100 hours to federal and congressional investigators about his work for Mr. Trump—including the coordination of hush-money deals with two women—he remained “a man all alone.”

“You would think that you would have folks, you know, stepping up and saying, ‘You know what, this guy’s lost everything,’” Mr. Cohen said during the March 25 call, recorded without Mr. Cohen’s knowledge by the actor and comedian Tom Arnold. Mr. Arnold, a vocal critic of President Trump who first made contact with Mr. Cohen in June, provided the recording to The Wall Street Journal for review.

“My family’s happiness, and my law license,” Mr. Cohen continued. “I lost my business…my insurance, my bank accounts, all for what? All for what? Because Trump, you know, had an affair with a porn star? That’s really what this is about.”

In pleading guilty in August, Mr. Cohen explicitly admitted to his crimes before a judge, to make it clear he was acting knowingly. “I take full responsibility for each act that I pled guilty to,” he said at his sentencing hearing in December. Since then, he has been attempting to have his sentence reduced by aiding congressional investigations.