Six defeats and a draw in their opening seven games have made for a demoralising start that earned former manager Paolo Di Canio the sack.
But Sunderland's new manager is convinced there is enough quality at the Stadium of Light to lift his struggling side off the bottom of the Premier League table.
The Uruguayan said: "I have no doubt. The idea is to believe. The key is to convince the players. They are the ones who need to feel on the pitch that they have got a chance to win the game.
"It's well-known in football that when you are at the bottom, you get no luck, no help, everything goes against you. We need to expect that, we need to be ready for that.
"Whatever happens, it doesn't matter. We need to keep believing that this is the way. I am responsible for that. The key is that they are convinced and they believe that is possible. We will see."
The 45-year-old, who has only had the opportunity to work with his full squad for the first time on Thursday, is also relishing the challenge ahead.
Poyet said: "I am happy and looking forward to it. In the situation we are in, I am not going to make any excuses. I am going to take whatever comes. This is where we are, we cannot complain.
"In the position we are in, we need to be respectful to everybody and show that we really care. That balance is not easy, especially for them.
"They have had one manager, an interim manager and then a new another manager. We are all different and they need to adapt.
"The quicker they adapt, the better for everyone."