Here's video of the moment Jeff Fisher told his Rams coaching staff he was just fired -- and Fisher was extremely emotional ... telling his coaches, "Sorry if I let you guys down."

The footage was shot during Week 14 of the 2016 NFL season (on or around Dec. 11) -- Fisher is breathing heavily and trying to collect himself before breaking the news in a team meeting room.

It's clear his staffers were completely blindsided by the announcement.

He promises he'll do everything he can to help get the other coaches new jobs.

In the video -- captured for this season's "All or Nothing" documentary on Amazon -- you can see assistant coach Mike Singletary walk up to Fisher to shake his hand and thank him. 

The Rams have since replaced Fisher with 31-year-old Sean McVay. Fisher is currently unemployed.