United have managed just two victories in their last 10 Premier League matches.
Mourinho served his second one-match touchline ban of the season on Wednesday as United beat West Ham 4-1 in the League Cup to set up a two-legged semi-final against Hull in January.
Success in knockout football, as Mourinho's predecessor Louis van Gaal discovered after winning last season's FA Cup, is not necessarily considered adequate at Old Trafford, though.
The statistics do not look good for Mourinho at present as their total of 20 points is their lowest at this stage of a season since 1989.
United have managed just two victories in their last 10 Premier League matches, and have just failed to win four home league games in a row for the first time since 1990.
Last Sunday's 1-1 draw at home to West Ham provided more headaches, which the cup victory over the same opponents three days later eased only partially.
United have been scoring freely in cup competitions, beating Feyenoord 4-0 in the Europa League within the last fortnight in addition to scoring four against West Ham.
It has been a different story in the league and Mourinho could do with a dominant display at Goodison Park to silence the critics.
"I am always expecting us to score goals, especially as we are playing so well," Mourinho said.
"Sometimes, when you are not playing well, you are just hoping that something happens for you to score a goal ? a set-piece, a corner, a mistake, an individual action.
"But this is not the case for us. We are playing so well and producing so much that the normal thing is to score goals and win matches.
"We are doing that in the cups. We scored four against Feyenoord, four against Fenerbahce, four against West Ham.
"In the Premier League, apart from scoring four against Leicester and three against Swansea, it was all about zeros and ones."
United will visit Goodison without suspended former Everton star Wayne Rooney, who has collected five domestic bookings.
Juan Mata, Zlatan Ibrahimovic and Anthony Martial are the candidates to lead United's attack this weekend.
Arguably of more concern is the absence of left-back Luke Shaw, who came off at half-time on Wednesday with a hamstring problem.
At least midfielders Paul Pogba and Marouane Fellaini are available to return after completing one-match suspensions of their own.
It seems a long time since Everton were second in the Premier League, yet it was as recently as September 17 that they occupied that position after collecting 13 points from their opening five matches.
The decline since then has been stark; a sequence of eight league games has brought only one win and six points.
Ronald Koeman's side have only fallen to seventh place, where they sit following last Sunday's 1-0 defeat at his former club Southampton.
More significant, though, is how close they are to falling much further; they are nine points adrift of the top four, but only eight points above the relegation zone as they head into the weekend.
Koeman needs some good news, and has it in the form of a near-full squad to pick from.
Only Muhamed Besic, still recovering from a knee injury sustained in a pre-season match against United at Old Trafford, is absent.
"First of all you need to work hard and that's the best way to turn things around," Koeman said.
"Still we are in a good position in the table and, if somebody had said to me at the beginning of the season that Everton at the beginning of December will be seventh and if they beat Manchester United we will go sixth, I would be happy."