The Toffees had three goals disallowed at the Hill Dickinson Stadium, but still came away with all three points thanks to goals from Idrissa Gana Gueye and Michael Keane.
It is the first time since September 2018 that Everton have beaten the Cottagers at home in the Premier League, having failed to win each of the previous four on home soil against the west London team.
“I thought we played well enough to win the game but Fulham were a threat,” Moyes told BBC Match of the Day after the final whistle.
“We justified the win. Even though it was 1-0, Fulham were a threat. I thought we grew back into the game and scored the second goal. Today it was tight, but we almost deserved it.”
David Moyes hails ‘fantastic’ Everton purchase of Dewsbury-Hall
Dewsbury-Hall was among the players who had a goal disallowed, but he provided the assist for Keane in an impressive performance from the midfielder. He has been one of Everton’s top performers since joining from Chelsea for £29 million this summer.
Moyes said: “He’s been fantastic for us by the way. He’s played so well and helped us play better this season.”
Thierno Barry also had a goal disallowed because the attacker, who signed a four-year deal with Villarreal this summer, is waiting for his first Premier League goal for the club.
“I was actually very happy with him today,” Moyes added. “Today was one of his better games. He’s just getting used to the Premier League and the intensity.”
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