Sunderland faces Aston Villa on New Year's Day and can move out of the bottom three with a win, which would also extend the club's Premier League unbeaten run to five games.
Poyet is delighted with his side's recent performances, but knows there is still a long way to go in the battle for survival.
"A few weeks or a few months ago, people were looking at the table and thinking it was impossible," Poyet told reporters. "And now we are there, so we have to make sure we don't stop and don't get complacent because we have done nothing."
Despite the warning, the Uruguayan praised his side for the timing of its revival and feels his side is building a pivotal rapport with the club's fans.
"I think it the unbeaten run has come at a great time," Poyet said. "I've always believed that Christmas is a key moment because there are so many games.
"I think the connection between the fans and the players is paying dividends. It's giving everybody that extra bit of energy and belief."
- Sports & Recreation
- Premier League
- Aston Villa