The holding midfielder lost out in a challenge with David Meyler which resulted in a goal and minutes later his back-pass found Matty Fryatt and he netted the third goal.
Prior to that point, Cattermole had been having another good game and Poyet, although disappointed with the overall result, refused to condemn the 25-year-old.
"The one who gives you everything, who is involved in everything, is the one who often makes a mistake," said Poyet.
"If you hide or are not in the game or do nothing to take a risk and try to win the game, then for sure you are not going to make any mistakes.
"That's the bad side of football.
"The ones who take responsibility and the ones who care - and show it week-in, week-out - are the ones in the position to make mistakes."