Poyet was sent to the stands by referee Mike Dean after kicking a container full of water bottles following the decision to book Jack Rodwell for simulation during the first half.
Sunderland, already trailing to Dame N'Doye's goal at this point, saw Poyet given his marching orders before the manager strode towards Bruce.
And an exchange of words - which Bruce said 'was not very pleasant' - saw the Hull manager then try and charge at Poyet, only to be restrained by officials.
Bruce was clearly disappointed in the behaviour of both himself and Poyet but said he would invite the Sunderland boss into his office for a post-match drink, after Jack Rodwell's late leveller ensured both sides shared the spoils.
"I don't know what I'm supposed to have done," Bruce said.
"We all do stupid things. Tomorrow morning we wake up to stupid headlines. To be fair, it was handbags. The big critical thing was I think Gus had seen it different, about Jack Rodwell diving, to gain an advantage.
"The referee got it right. And I think, obviously by his reaction to that, he must have seen it the other way. That was that really.
"I don't know what I'm supposed to have done, because I only went to his assistant and said 'Rodwell had dived'. That's all I had said.
"We'll invite him in and hope he has a glass of red. I hope so. I hope he comes in. What goes on the pitch, for me, what goes on out there…we'll both regret it in the morning and we'll just get on with our lives."
Bruce thanked the assistant referee to getting between him and Poyet and said: "I'll have to go and buy him a beer.
"[I'm] a big heavyweight, and he was a little bit of a lightweight to be fair to him. I think he was exhausted after trying to keep ahold of me."
Bruce was pressed numerous times for details on what Poyet said in his press conference and eventually revealed that it was far from courteous.
"I think it's right that I keep it to myself. It's up to Gus. If he wants to reveal why I've gone on like some raging idiot, then it's up to him," he said.
"I'm sure everyone will now be lipreading to see what he said to me. But it wasn't very pleasant, like 'have a nice afternoon, Steve' or 'have a nice evening, Steve'."
On the result itself, the Hull boss added: "I thought we did enough. I thought we had the best opportunities. That's where we are disappointed - not with my antics.
"We've had two, three, four, really good opportunities without my goalkeeper having to make a save, really.
"I thought we played very, very well. We needed the second to go in [though] and unfortunately it didn't."
