5:19 PM PT -- We spoke with Spence after the wild press conference ... and he said Bud's fiery response to his supporters was "irrational," since he didn't react when Crawford's team was chirping at him.
"He shouldn't have done that," Spence told TMZ Sports. "His people were saying crazy stuff ... I just turned around and smiled. I didn't turn around and say something crazy or argue with his family."
"Regardless of if I argue or not, they're gonna think the same thing that they've been thinking."
Terence "Bud" Crawford just lost his cool on an Errol Spence supporter ... repeatedly calling the man a "bitch" and a "ho."
The fiery scene played out toward the end of the boxers' prefight press conference Thursday afternoon in Las Vegas ... when someone who appeared to be in Spence's camp began chirpin' at Crawford from their front row seat.
It's unclear exactly what the agitator said ... but it ticked off Crawford, who paused everything on the stage to fire off insults at the man.
"You a bitch, n****!" Crawford said. "F*** you talkin' to?! You a bitch, n****, 'cause you keep talkin' like a bitch n****! You doin' all that talkin'!"
The 39-0 fighter kept the verbal jabs flying for several more seconds ... before, mercifully, it ended.
As for Spence ... he seemed to be amused by the situation, even joking with the guys if they were done so he could continue talking.
The entire event was filled with tension ... as the two fighters' trainers even got into a verbal spat while at the podium.
Hecklers in the audience, meanwhile, could be heard yelling at the boxers throughout it all as well.
This is probably the most trash talking we've seen from both sides since the two agreed to fight ... and it's something boxing fans have been waiting for.
Saturday night's tilt on Showtime PPV at 8PM ET/5PM PT can't come soon enough!