The 45-year-old Uruguayan will send his team out for the first time at Swansea on Saturday still awaiting a first league win of the season and already six points adrift of safety.
Six defeats and a single draw in their opening seven fixtures have made for a demoralising start and served to catapult former manager Paolo Di Canio through the exit door at the Stadium of Light.
However, replacement Poyet is convinced there is enough quality within the dressing room to get the Black Cats out of trouble, and his first mission will be to persuade the players that is the case.
He 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 chaos of the Di Canio era and a fixture list which sent Liverpool and Manchester United to Wearside on successive weekends before the international break have done Sunderland few favours.
Things are set to get little easier during the opening weeks of Poyet's tenure with the trip to the Liberty Stadium coming eight days before the derby clash with Newcastle at the Stadium of Light.
However, the former Brighton manager is relishing what lies ahead and insists he will not be looking for excuses if events do not unfold as he would like them to straight away, having only had the opportunity to work with his full squad for the first time on Thursday.
He 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. I am not going to be saying we have only had nine days or 10 days. Remind me if I say that after the game.
"But it's true, I cannot complain. I wanted to take this opportunity and be here, so now I cannot change. This is where we are.
"I hope we can show that things are going to work better. The players, they are good. We are trying to make sure that they are not confused by too many changes.
"We are trying to make them understand that there is a part of the [training] session that, we are normal people and we can enjoy, and there is another part that is business and it's serious.
"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."
Poyet will have a virtually full squad from which to choose this weekend with Phil Bardsley, Wes Brown and Steven Fletcher all back in contention, although midfielder Ki Sung-yueng will miss out under the terms of his loan agreement with Swansea.
Ki will be available once again for the derby, but Poyet is not even allowing himself to think about that game just yet.
He said: "For me, it's incredible because everybody keeps talking about it. I need to forget about it and think about Swansea. We will talk about that next week."