Having comfortably seen off West Ham United in front of the watching Sam Allardyce on Wednesday night, Everton made it back-to-back wins - and clean sheets - with a 2-0 victory over Huddersfield Town in the new manager's first game in charge on Saturday.
"The changing room is a lot happier place after the game," said Williams. “We've had two games in four days, two wins and two clean sheets, and you can't really ask for much more than that.
“We've needed some clean sheets and to get two on the bounce is nice. When you don't concede you give yourself a chance to win the game and that's what we've done.
“We've had two training sessions with the new manager and one match. He hasn't changed too much, he's just tried to give us a few of his ideas about how he wants us to play.
“We've got the Europa League game now and then the derby. There's no better preparation than two wins before those games and I think momentum and confidence is big in football.
“We're trying to get a little bit of that and keep it going for as long as possible."