The win over Watford, achieved thanks to goals from Oumar Niasse, Dominic Calvert-Lewin and Leighton Baines, saw Everton climb to 15th and Unsworth said now was the time to kick on.
"I've said to the players after the game, this must kick start them. This must instil some confidence and belief moving forwards," Unsworth told the club's website.
"Confidence is key. It's a word that gets bandied around in football all the time but it's true - as a player, when you're playing full of confidence, you feel unstoppable. Hopefully that's the start of a good run for us now."
The 44-year-old also praised the fans for their support and said Sunday's win was "full of heart and character and desire".
Everton's next league game is a visit to bottom side Crystal Palace on Nov. 18.
(Reporting by Aditi Prakash in Bengaluru; Editing by Peter Rutherford)
