Poyet was furious at referee Andre Marriner's decision to send off Cattermole, while failing to punish Hull's Paul McShane for a challenge that "could have killed" goalkeeper Keiren Westwood.
He 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.
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."
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