Manchester United romped home thanks to goals from Antonio Valencia, Henrikh Mkhitaryan, Romelu Lukaku and Anthony Martial.
They also secured their fourth clean sheet in five Premier League matches this season.
But Neville thinks Mourinho will be uneasy about his team’s ability at the back.
“He’ll be a little bit concerned about the goals they conceded at Stoke last week and a couple of good chances they conceded today,” he said on Sky Sports.
“United haven’t played what I consider the best teams in the league yet, so they will be a little bit concerned.
“But there is a pattern building of a team finishing games off that they didn’t finish off last season.”
Mourinho thought his side turned in their best display of the campaign.
He said: "I think the performance was very good, especially in the first 30-35 minutes, it was probably our best performance of the season.
"We pressed them and they did not have a chance to get out, they did not have a shot, it was very impressive.
"After that, Everton's good players came out and showed their qualities.
"They gave us difficulty but I looked behind me on the bench and saw alternatives."
