Mourinho salutes 'top class' Man United
The victory at Goodison Park brought an end to a run of three successive draws in the Premier League over the festive period, with United looking a lot sharper at the start of 2018.
Anthony Martial led the line in place of the injured Romelu Lukaku and scored the opening goal early in the second half with a fine strike, before Jesse Lingard sealed the win late on with a similarly impressive effort.
Mourinho was so happy with the performance that even without the win, he would have been "proud".
"The boys deserve it," Mourinho told Sky Sports. "I keep saying that the draws have not been bad performances, because there were situations that have made it more difficult for us.
FT - Everton 0 #MUFC 2.
Brilliant goals from @AnthonyMartial and @JesseLingard hand the Reds a deserved victory, and the perfect start to 2018! pic.twitter.com/tbBKwoMM3x
— Manchester United (@ManUtd) January 1, 2018
"We made our mistakes, especially in games against Leicester and Burnley, but the attitude, effort and pride were fantastic.
"Everything was top class. I think we played very well. It didn't look like a tired performance or the sort of performance [you might expect] after the worst possible calendar you [the Premier League] give to us.
"Okay, Everton had a reaction in the second half, but we were always in control. I'm really pleased with the points. Even without points, I'd be proud of what the boys did."
Lingard was particularly effective once again – his six Premier League goals since the start of December are only bettered by Harry Kane's eight - and Mourinho believes he is starting to reach his potential.
He said: "These boys, they jump or they do not jump. It is one thing to be a young talent and another to be a very good player.
"Some players aren't capable of that jump. They go from having great potential as a young player, to becoming normal players.
"I think Jesse is making that jump. He's more consistent, understanding the game and different positions more. I think he's going in a good direction."
Mourinho also hinted United may opt to bring in reinforcements in the January transfer window due to an injury list which has them "in trouble".
"I don't know, honestly," he said. "I know in this moment we are in trouble, but maybe in two or three weeks we recover more players and we think differently and wait until the summer to try things, but I cannot say now."