Zlatan Ibrahimovic saw a 71st-minute equaliser ruled out for offside, with replays suggesting he may have been onside before he headed the ball past Everton goalkeeper Joel Robles.
He eventually did level with a stoppage-time penalty, cancelling out Phil Jagielka’s 22nd-minute opener, but Mourinho said United had been denied victory unjustly.
“With the VAR (video assistant referee), we win this game 2-1 because it’s not an offside,” Mourinho told BT Sport at Old Trafford.
“But it’s a difficult one for the linesman. I’m not critical of the linesman. I just say when the VAR comes, it will help everyone, especially the linesmen and referees.”
Video technology, which enables officials to overturn match-changing decisions after consulting video replays, is currently being trialled internationally, but is not in use in the Premier League.
Ibrahimovic’s 94th-minute penalty, after Ashley Williams was sent off for handling substitute Luke Shaw’s goal-bound shot, extended United’s unbeaten run to 20 league games.
But it was their ninth home draw of the campaign and left them four points adrift of Manchester City, who occupy the fourth and final Champions League qualifying berth.
“The performance was not very good,” said Mourinho, whose side drew 0-0 at home to West Bromwich Albion on Saturday.
“The spirit in the second half was phenomenal, with some players really in trouble.
“Some by the physical point of view, some others clearly with the confidence level low and difficult to perform better. But they fought until the last second.”
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