However, Poyet has warned everybody connected with the club that there is still a lot of work to be done.
"Everything is big today. It's a first win against our biggest rivals in our first home game. The fans are going to be delighted and the players will be relieved. We needed this," he told BBC Sport. "It gives us everything. We needed something. Now there are no excuses, we can go next week and win another game and continue to improve.
"This will change our season. I'm sure the players will be even more together and the fans will look forward to the next game. We have done nothing, it was nice for us and the fans but we need to keep winning games."
Next up for Poyet's team is a trip to Hull City on Saturday.