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First they boo'd the team ... then Pats fans FOUGHT EACH OTHER after Tom Brady's squad lost to the Chiefs -- and it's all on video.

It was peak embarrassment at Gillette Stadium where even the TV announcers calling the game clowned Pats fans for having the audacity to BOO while the team was down at halftime.

But, it got even worse AFTER the game, when a couple of Pats fans in the disappointed crowd turned on each other and began throwing punches right in the stands.

At one point, one of the combatants took TWO left-handed bombs to the face ... and you can hear in the audio, people were pretty disgusted by the scrap.

Unclear how the issues were resolved ... we're still waiting to hear back from the Foxborough Police Dept.

As for the Pats on the field ... it's understandable why some fans are going crazy after their games these days -- Brady and the guys look NOTHING like future Super Bowl champs.

Still, 10 Super Bowl appearances in 20 years with 6 NFL titles ... oh, and they're 10-3 this season, heading to the playoffs AGAIN! Calm down, Beantown!!!!!

Meanwhile, Tom's already claimed the team is focusing on next week's game against Cincinnati ... so, sorry, Andy Dalton.