The Black Cats produced a 2-1 victory at the Stadium of Light to record their first triumph of the campaign and new manager Poyet has urged the squad to take heart after getting off the bottom of the table.
"Look, I didn't like to see the table. When you are bottom, it's not nice. We are off the bottom - that's something; we beat the biggest rivals - that's even bigger,â€ť he said.
"Now we need to keep going. We need to start passing the ball better, we need to keep believing and we need to do different things.
"This is what we needed so, from now on, there are no excuses because we needed a lift and there is no better lift than this one, so I am very happy for the players and absolutely delighted for the fans.
"I saw what it means all this week in town. I imagine how it is going to be this week - I don't know how much it matters being second from bottom, it's just about beating the rivals and everyone will have a nice week, I will tell you that."
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