The 25-year-old has been playing in defensive midfield under the Uruguayan, a position that has earned him plaudits from his new boss.
Cattermole was sent off against Hull City in November, the seventh red of his Premier League career, however Poyet believes this is part and parcel of the midfielder's game.
"The game against Hull, he was one of our best players but then he picked up the red card - that is Lee Cattermole as well," Poyet told the Sunderland Echo.
"Everyone has opinions but, for me, I have no words high enough to praise him.
"My first game in charge, the game at Swansea, the best player for us? Lee Cattermole.
"The next game, the derby against Newcastle United, for that first hour against them he was the perfect player to have on the pitch in a derby game.
"During his suspension, we started to play OK, so he had to wait for his chance to get back in, but he got back in against West Ham and was one of our best players.
"And then he goes on to play against Chelsea in the cup on Tuesday and was, in my view, man of the match.
"Ki played very well in the defensive midfield role, but sometimes, when someone plays as well as Lee has been, you have to find a place in your side for him."