Mayor Bill de Blasio on Thursday disputed NYPD widow Leanne Simon­sen’s stance that “trigger-happy” cops led to friendly fire tragedies like her husband’s — but admitted the department needs new training.

“She’s a very good person and she’s speaking out of real personal pain,” de Blasio said of Simonsen, who told The Post in an exclusive interview Wednesday she felt that cops’ itchy trigger fingers contributed to the February loss of her husband, Queens Detective Brian Simonsen, and the Sunday death of Bronx cop Brian Mulkeen.

“My experience has been very different over now six years, having seen so many situations and a lot of body camera footage and other footage where officers showed extraordinary restraint,” said de Blasio, speaking at an unrelated event hours before he attended Mulkeen’s wake in upstate Monroe.

But de Blasio agreed with Mrs. Simonsen: Retraining is needed.

“There’s a real issue. We lost two of our officers,” the mayor said. “It means by definition we have to keep understanding what the NYPD can do better, and I think training is always part of the solution.”

Uniformed cops were ordered to take “an enhanced one-day training course focused on the response to critical incidents” after Simonsen died in a hail of 42 police bullets while responding to a chaotic cellphone store stickup by a suspect who it turned out was armed with an imitation gun.

Tragedy struck again early Sunday as Mulkeen was fatally shot by fellow cops while wrestling for control of his service weapon with an ex-con in the Bronx.

Police Commissioner James O’Neill has vowed that the department “can learn from this.”

Hizzoner was adamant Thursday that it’s not a matter of “can,” but rather “must.”

“We are going through a full review and . . . [will] determine what needs to change in training,” he said. “And clearly there has to be some additional approach to training here, and we have to get that right.”

Plainclothes cops are being mandated to attend “enhanced tactical training” following Mulkeen’s death, NYPD sources said.

De Blasio said that despite the friendly fire deaths — accounting for both fatal line-of-duty cop shootings this year — he believes the foundation for change has already been laid.

“I think that the training that has occurred — started by [former] Commissioner [Bill] Bratton and deepened by Commissioner O’Neill — has emphasized de-escalation, restraint of use of weapons, a whole host of things that made the NYPD better,” said de Blasio.

“Overall I think the big picture is, every time we’ve invested in training it’s had a very powerful impact . . . and we’re going to do more.”