Erik ten Hag's side suffered a major blow to their hopes of a top-four finish in the Premier League as Alex Iwobi snatched Fulham's winner seven minutes into stoppage time.
United defender Maguire looked to have rescued a point when his close-range finish in the 89th minute cancelled out Calvin Bassey's 65th-minute opener.
But United were caught throwing players forward in search of all three points as Iwobi capped a counter-attack to seal Fulham's first victory at Old Trafford since 2003.
"Overall on the balance of play we didn't do enough in the first 60 minutes or so. We started the game not great," Maguire said.
"The first half was pretty even, but when you're not playing at your best you have to do the basics right.
"To be a goal behind, I thought our reaction was brilliant, especially in the last 30 minutes and when we equalised probably only one team was going to win it.
"We were probably naive in the end by throwing too many bodies forward and getting done on the counterattack."
Sixth-placed United are now eight points adrift of fourth-placed Aston Villa in the race to qualify for next season's Champions League.
United could have no complaints after Fulham dominated with a display that punctured the optimism around Old Trafford following the confirmation of Jim Ratcliffe's purchase of a 25 per cent stake in the club this week.
British billionaire Ratcliffe, a boyhood United fan, has taken control of the club's football operations from unpopular owners the Glazer family.
But United's tame performance underlined how much work they have to do to fulfil Ratcliffe's bold ambition of knocking Manchester City and Liverpool "off their perch".
Maguire claimed United were hampered by the absence of Denmark striker Rasmus Hojlund, who had been in fine form before suffering an injury this week.
"We got hit by the injury to Rasmus, who has been big focal point for us. But it is up to us to find the solutions and the areas we need to improve on," Maguire said.
"We can play into him, he holds it up, he starts the press really well, not only that but Marcus (Rashford) has been playing really well on the left.
"It's the story of our season, we've been injury hit, as other teams have, and we need to find a solution quick."