Cattermole convinced Sunderland will be safe under Poyet
Poyet replaced Paolo Di Canio at the Stadium of Light in September but, despite improvements in performance, Sunderland will be bottom of the Barclays Premier League on Christmas Day.
"All we can do is take confidence from that game," said Cattermole.
"The manager said it is the best performance he has seen from his Sunderland side - we controlled the game throughout. The message from the manager is that if we play like that for the rest of the season we will have no worries."