In response to reports of the mass gathering of mourners, Mr de Blasio warned "the Jewish community" that police would make arrests.
The city leader was accused of anti-Semitism for his comments.
The Hasidic Jews were mourning a late rabbi at the service in the Williamsburg, Brooklyn, neighbourhood.
"If in my passion and in my emotion I said something that was hurtful, I'm sorry about that," Mr de Blasio said.
"I have no regrets about calling out this danger and saying we're going to deal with it very, very aggressively."
Images shared online by journalists show a large gathering of people attending the funeral on Tuesday night.
Mr de Blasio's original comments called the crowd "absolutely unacceptable".
"When I heard, I went there myself to ensure the crowd was dispersed," he said. "What I saw will not be tolerated so long as we are fighting the coronavirus."
But it was his subsequent tweet, in which he singled out "the Jewish community", that drew ire.
"The few who don't social distance should be called out," said Anti-Defamation League CEO Jonathan Greenblatt on Twitter.
"But generalizing against the whole population is outrageous especially when so many are scapegoating Jews."
And the American Jewish Committee said: "The vast majority of the Jewish community is following the guidelines.
"You can find us donating blood, raising money to support our neighbours, and in emergency rooms providing critical care. We deserve better from our leaders than generalizations and finger-pointing."
After apologising for his comments, Mr de Blasio said he "understood" that people were in pain, but there were consequences for those who attended.
"Some will be sick with that disease," he said. "It's just a fact, we know this.
"Some will spread the disease to others. People, as a result, will die."
It is not known how many people attended the funeral.