"I'll tell you it's very frustrating," Hoffmann told Babcock on the "TMZ Sports" TV show (airs nightly on FS1) ... "it just really pisses you off that this happened."

The longtime USSS special agent added ... "Sometimes everybody says 'things happen,' but this is something that just can't happen. This is inexcusable. And it's something that everybody needs to take a real hard dive at and look into this."

If you're not familiar with Hoffmann, he was a star linebacker at the University of Washington, leading the Huskies to a national championship in 1991, before being drafted by the Chicago Bears in 1993. After a couple of seasons in the NFL, David hung up his pads ... trading them in for a badge.

Hoffmann spent 23 years with the United States Secret Service -- protecting Bill Clinton and George W. Bush, among others -- before retiring from the federal law enforcement agency in 2021.

In the aftermath of the Butler, PA assassination attempt, many questioned whether the Secret Service screwed up, and instead of focusing on its main objective (keeping POTUS safe), the agency let other factors come into play, creating a potentially dangerous situation.

"I think everybody would agree with putting the best people out there, having tryouts for everything, having to make these teams," David explained.

"And that's why it was a treat for me to be a part of the counter-assault team. You always had to perform. You were tested. You had to show performance. physically, mentally, emotionally. And that's something I think should be across the board."

FYI, USSS describes "CAT" as a "specialized unit within the U.S. Secret Service that provides full-time, global tactical support to the Presidential Protective Division."

Check out the full clip with Hoffmann -- there's a lot more.

We also talked to David about the agents who rushed the stage and jumped on Trump, as bullets flew their way ... in addition to whether the agency would typically account for an elevated firing position with a clear shot at the president.