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8:45 AM PT -- Sources connected to Pete tell us he felt like Vinnie was overly sarcastic when he told the crowd not to mention Kate or Ariana. They add, Vinnie asked if he could do an opening set, but Pete said no -- because he travels with his own opening comic -- but Vinnie went ahead and did a 5-minute set anyway.

Overall, we're told Pete's camp thinks Vinnie killed the energy in the crowd by giving them the list of no-no's for the show.

Pete Davidson is going to war with a comedy club owner because the guy referred to Kate Beckinsale and Ariana Grande while introducing Pete -- however, the crowd seemed to turn on Pete.

The 'SNL' star was supposed to perform Monday night at Vinnie Brand's Stress Factory in Bridgeport, CT -- but he never made it onstage. Pete claims Vinnie "disrespected me and did something that I told him not to do and I can't perform under those circumstances."

Pete posted a video from his car immediately after bailing on the gig.

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Meanwhile, inside the club ... the owner was fuming over Pete's no-show -- and played Pete's IG video on the club's big screen. Even though Pete offered to do a free show for anyone in the crowd ... they were pissed. You even hear someone yell, "F**k you, Pete!!!"

According to clubgoers, Vinnie did mention Kate and Ariana -- but only because he was asking the crowd not to heckle Pete about his girlfriends. Vinnie says those were the ground rules Pete wanted, and they had agreed anyone who did shout anything like that would be removed from the club.

It seems both Pete and Vinnie didn't want a repeat of what happened during one of Pete's shows back in February ... when he was heckled about Mac Miller.

Vinnie did his own act after playing Pete's IG video -- and while it wasn't necessarily funny, it was very angry.