Colbert dove into the big story around his office during Monday night's episode of 'The Late Show' ... explaining everything that led up to the big bust in Washington. As we reported, cops busted 9 of his staffers -- including Robert Smigel, who typically has his hand up Triumph's ass -- while they were recording bits Thursday evening in the hallways of Congressional offices.

Doesn't sound like SC holds any grudges ... as he put it, the CPD officers were just doing their jobs, and so were my staff -- and he even acknowledged the fact Capitol Police have to be a bit more on edge since Jan. 6, 2021.

But, he says the whole story went haywire for him when he started seeing headlines about Triumph pulling off a Capitol insurrection 2.0!

While laughing, but also genuinely shocked, he points out ... "An insurrection involves interrupting the lawful action of Congress and howling for the blood of elected leaders, all to prevent the peaceful transfer of power."

He added all Triumph and co. were doing was "First-degree puppetry!!! This was hijinks with intent to goof." Hilariously, he admits cops should ring them up on charges for "Misappropriation of an old Conan [O'Brien] bit."

The 'Late Show' staff had been shooting outside the offices of House Minority Leader Kevin McCarthy and Rep. Lauren Boebert -- and cops say they didn't have proper ID to be there on their own.