Poyet said: "This was a proper game in this division and, with none of the top 12 winning, we hope it's a turning point in terms of victories.
"I want us to be there at the beginning of April and it's totally up to us. It was important today and the players fought for it.
Poyet had no doubt that former Manchester United goalkeeper Tomasz Kuszczak played a vital role in only his team's third win in the last 11 league outings by producing two superb second-half saves.
The Uruguayan added: "Tomasz had the chance to show what he is all about and you need that kind of reaction. He produced two very good saves and the clean sheet was all-important."