The Black Cats are yet to win in the Premier League this campaign and have drawn four of their opening five matches.
However, Poyet believes that once his side find their form, it will give them the confidence to put together a winning run.
"We are heading in the right direction," the Daily Star quotes Poyet as saying.
"I am confident the players are happy, they know their roles in the team and I have plenty of options.
"I have the belief that we are very close and when it starts going our way, we could easily win three games in a row."
Sunderland will host Swansea City in the Premier League this afternoon.