Jack Rodwell's controversial 77th-minute equaliser - which saw the ball strike his arm - won a point for Sunderland after Dame N'Doye gave Hull an early lead.
But the post-match talk focused on Poyet's confrontation with Bruce, which began after the Uruguayan was sent to the stands for kicking a container full of water bottles. That was in response to a decision that saw Rodwell booked for simulation.
Before leaving the pitch, Poyet headed for Bruce and the latter tried to charge at him, only to be restrained by a match official.
Poyet said he would visit Bruce's office for a glass of wine following his media commitments, though, and he may have raised the conduct of McShane with the Hull manager.
When asked if he would reveal the conversation between the two, Poyet said: "No, because I am old-fashioned. I don't want technology in football and what happens on the pitch, stays on the pitch.
"No problem [with Steve]. I will take it [a glass of wine]. I just saw him and nothing happened. It's football... passion.
"Kicking a bucket of bottles of water, I don't think is nothing serious. I understand it doesn't look good, especially if 20 bottles are coming out of the bucket. I was quite good at kicking with my right foot, unfortunately.
"I was not happy with the decision on McShane [though].
"[He was] diving like he was in a theatre dancing ballet and he lost his foot, and getting a free-kick for Hull. And then Jack diving and getting a yellow card and a free-kick against. Give me one. You cannot have both go against you.
"Have a look on TV, if they can show it, McShane, in the first half, jumping in with two feet and going down like he had been shot, but he won a free-kick.
"And then the other way, [it] is a free-kick for them as well and a yellow card. I just was asking for the same treatment."
Poyet said he did not intend to provoke Bruce when he walked towards him after being sent off by referee Mike Dean.
He did concede it had been a tough few days, though, in the wake of Adam Johnson's arrest on Monday.
When quizzed about the charges against Johnson, Poyet said: "The only thing I can tell you was that it was a very difficult day. I never had one like that. Very difficult."
