The midfielder, who had reportedly fallen out with previous manager Paolo Di Canio, was given a straight red card by referee Andre Marriner after a late tackle on Ahmed Elmohamady in first-half stoppage time.
And he was followed down the tunnel just two minutes later by team-mate Andrea Dossena, who unleashed a crude stamp on the shin of Hull midfielder David Meyler, leaving Sunderland with nine men.
After the match Poyet openly criticised Marriner's decision to send Cattermole off, claiming that the former Wigan Athletic man's reputation earned him his marching orders.
He told Sky Sports: "I'm convinced it wasn't a red card. I think sometimes people just see Lee Cattermole making a tackle and that's it.
"I think we need to be fair to him. It's Lee Cattermole. People put things in the mind of (referees)."
Hull clinched the win in the 25th minute as Liam Rosenior's right-wing cross was diverted past Keiren Westwood by his own team-mate Carlos Cuellar, but Poyet was pleased still with the efforts of his team.
"It was a very strange game," he added. "Too many things happened. Too many decisions to make for players, referees, managers.
"It was a proper Premier League game that somehow only finished 1-0. It could have been different. If Adam Johnson had scored, if Harper hadn't have managed to save it, it could have been different.
"But I'm very proud of the players. They played well in the first half and hung on in the second half when it was difficult for them."
