The Black Cats had a nightmare first half in their 1-0 defeat at the KC Stadium, with Carlos Cuellar scoring a decisive own-goal before Cattermole and Andrea Dossena both saw red just before the interval.
Poyet accepted Dossena had to go for a dreadful stamp on David Meyler but felt the eighth red card of Cattermole's career - for a studs up tackle on Ahmed Elmohamady - was a harsh one.
His feeling of injustice was aggravated by the fact McShane was not penalised for his collision with Westwood, which left the Irishman groggy and unable to continue.
Poyet accepted there was no malice in the challenge but gave a colourful account of the danger involved.
Asked about the dismissals, he said: "Cattermole no, Dossena yes.
"I would love the ref to talk. If I was a pundit working today - and I was during the summer when I was out of work - I would ask the technical people to show the tackle on Westwood that nearly cut his head off, the one on Adam Johnson (by Robbie Brady) and the one from Lee Cattermole and let the pundits comment on them.
"They need to comment on all the tackles. I'm not accusing McShane at all: I think he played the ball and he was late but he nearly killed him and he is injured and he is out and I need to change my goalkeeper.
"The tackle of Lee didn't touch him (Elmohamady). He was still on the pitch and he was down for two minutes, there's a little bit of a difference,
"Maybe I'm from another planet, I don't know."
Tigers boss Steve Bruce, who was facing former club Sunderland for the first time since his sacking in 2011, knows all about managing Cattermole's feisty side.
He coached the midfielder on Wearside and earlier at Wigan but felt his sending off this time was correct given current regulations.
"Thankfully he's not mine to manage anymore," he said.
"(But) we all know what I think of Lee as a player. One thing Lee's got to curb is that red mist that comes down. We know you can't make that challenge in today's football, you just can't make it.
"He's got to learn that and I'm sure he will...eventually.
"In my day it might have been a booking but the directive is that if you leave the floor with studs showing, even if you don't make contact, it is seen as reckless and endangering the the player.
"The referee's got that one right and the second one (by Dossena) is a horror challenge, let me tell you.
"It was on David Meyler, who has had two serious injuries in his career, and he was lucky because those are the ones that really damage footballers.
"I don't know if you can get three red cards but he deserved them."
Bruce, who suggested before the match that his decision to take the Sunderland job in 2009 was a mistake due to his Newcastle roots, denied he took any undue pleasure from the result.
"You all want the story, I understand that, but as far as I'm concerned it's gone; history," he said.
"Let's all move on with our lives, it was a long time ago. No matter who you managed, when you get one over an old team it's always satisfying but that's about it."