The Black Cats are still searching for their first win of the campaign after Poyet's first match in charge ended with a 4-0 defeat at Swansea City last weekend.
He told The Mirror: "On one side, we have time. I don't want to go to the other side and say this is a final. It's about winning a football game. And it needs to be now.
"Can we do it? I believe. And we are going to work so hard this week that it is possible. I know what we need to work on, but I don't know how quickly it will work. I can't tell people it will work in five days or a month.
"I hope it works really quickly. We can't lose many more times. I'm not going to say names, but there were players who reacted in a good way to the first goal and players who reacted in a different way. It's true I have a better picture for next week."
The Uruguayan now has a week to prepare for the season's first Tyne-Wear derby, with Newcastle United due at the Stadium of Light on Sunday afternoon.