Moyes's side face fellow strugglers Hull at the Stadium of Light on Saturday, and he is hopeful that brighter times are ahead for the team and the fans.
"We've had a good couple of weeks and it felt good to win again. We've had great support and we want to keep winning," he told reporters.
"I'm hoping we've put all the injuries behind us. The players are in good spirits and we want to do it again. We need to give the supporters something to shout about and we haven't done enough of that this year. Hopefully we can tomorrow.
"Sometimes in adversity it works for you. It looked like a difficult pre-season but [Hull] have done really well. They have won some big games. I watched their last game and they picked up an important three points."