The Uruguayan boss watched his side go down to nine men but he did not believe that Cattermole should have been dismissed.
Poyet also thought Hull's Paul McShane should have been punished for a challenge on keeper Keiren Westwood which he claimed "could have killed him" after the Republic of Ireland international had to be replaced in the first half following the challenge.
"I'm not accusing McShane at all," said Poyet.
"I think he played the ball and he was late but he nearly killed him and [Westwood] is injured and he is out and I need to change my goalkeeper.
"The tackle of Lee didn't touch [Ahmed Elmohamady]. He was still on the pitch and he was down for two minutes - there's a little bit of a difference."