Bruce had to be restrained as the pair squared up moments after Poyet was sent off for reacting badly to midfielder Jack Rodwell's yellow card.
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Bruce blamed the incident on the "heat of the moment" while Poyet said: "What happens on the pitch stays there."
Dame N'Doye gave Hull a first-half lead before Rodwell equalised on 77 minutes.
Rodwell was booked for simulation with his side trailing 1-0 at the KC Stadium, prompting Poyet's furious reaction.
"I was sent off for kicking the bucket," he told BBC Sport.
"I know it doesn't look good, but it's nothing to worry about. I prefer that than saying something I would regret."
After Poyet was sent to the stand by referee Mike Dean, the Uruguayan walked across to confront Bruce.
The pair exchanged words before Bruce had to be restrained by an assistant referee and members of his coaching staff.
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"I don't know what I was supposed to have done," said Bruce. "He obviously feels aggrieved about something."
Bruce added he would let Poyet explain why he reacted the way he did, but insisted Rodwell had dived.
"The ref has seen it," said Bruce. "From Gus's reaction, it looks as though he didn't agree."
Rodwell's header kept Sunderland in 16th place in the Premier League on 26 points, four above the relegation zone.
Hull have 27 points and are 15th in the table with 10 games to play.
Poyet was also asked about Adam Johnson after the game.
The Sunderland winger was arrested on Monday on suspicion of having sexual activity with a 15-year-old girl and subsequently suspended by the club "pending the outcome of a police investigation".
Durham Police said Johnson, 27, was questioned at a station close to his County Durham home and later bailed.
Poyet said: "The only thing I can tell you is that it was a very difficult day yesterday. Very difficult day. I never had one like that, very difficult."
Hull City manager Steve Bruce described his confrontation with Sunderland boss Gus Poyet during their sides' 1-1 draw as "grown men acting like children".