United came into the game eight league games unbeaten under interim boss Ole Gunnar Solskjaer and took the lead after just 14 minutes, with the rejuvenated Paul Pogba scoring a fine effort at the near post.
Pogba stole the show but Martial impressed on his recall with Diogo Dalot, Phil Jones and Chris Smalling helping to keep a clean sheet after coming back into the side, with Romelu Lukaku and Juan Mata also given a chance to impress.
"We gave them the first 10 minutes, maybe played into their hands".
"It will be the big games coming up now that decide where we end the season".
Solskjaer said he had met United owner Avram Glazer after the game, but he wouldn't be drawn on whether they would have any further meetings to discuss his future at the club.
"I've just spoken to him outside", he said.
"I've been in that situation a few times myself and it's about who grabs it. I have to say I don't think I would have hit it like he did, so fantastic goal".
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"(Being in the top four) is a big thing", conceded Solskjaer. We've talked about this - how we wanted to be in the top four and although there is still a long way to go, we are there and we want to stay there.
Ranieri felt his players lacked the composure at 1-0 down to get themselves back into the game against such talented opposition.
The crowd, unimpressed at the Schuerrle substitution and the very late introduction of promotion heroes Ryan Sessegnon and Tom Cairney, booed Fulham manager Claudio Ranieri off at the end of the match.
As for his goal double against Fulham, Pogba said: "It's always great to score goals, most important is to win games".
"But my players are very.... not anxious, but they want to score immediately to draw the match and against big teams that is hard and we conceded to them the counter-attack". We conceded the counter-attack, and at that point it was more hard. "We could have had four or five goals, it was different to what we did against Leicester so another step in the right direction".
"When you play against champions, you have to stay calm, don't lose your composure".
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