Reading have endured a difficult time since they returned to the top-flight and host Fulham on Saturday having picked up just three points from their opening seven games.
The Berkshire club have squandered leads twice in both their games against Swansea and Newcastle while they were completely outplayed in their home defeat to Tottenham.
If results go against them this weekend, McDermott's team could be five points adrift of safety come Sunday night, but the Reading boss wants the Royals faithful to keep backing the side.
"We really need the fans. They have to believe (in us)," McDermott said.
"They have been important to us since I became manager. They have stuck by us when times have been difficult. Now we are going through a difficult spell of results but they can really pull us through.
"Everyone knows the Madejski Stadium is a very difficult place to come and get a result and the fans are a big part of that.
"I'm sure they do believe that we can do whatever we have to do in this league."
Reading striker Jason Roberts thrust himself in to the spotlight last weekend when he refused to wear a Kick It Out shirt in the warm-up before the Royals' 1-0 defeat to Liverpool.
The 34-year-old will continue his protest at the football authorities by not wearing the T-shirt again before Saturday's game, but he wants to put talk of the boycott to one side now and start concentrating on helping the team pick up their first win.
The former Blackburn striker has been encouraged by recent performances from the team and thinks it will not be long before they achieve their first victory.
"The performances have been better than the results, but that's the Premier League for you," he said.
"As a group we are new to this league, but we have a strong squad.
"We are disappointed with the results but we believe that will change.
"We believe in each other's ability and we have a good chance of turning things around. That first win is on its way."
Roberts' frustration does not extend to McDermott, who has overlooked him for a starting berth this season.
"I had a bit of a calf problem which has taken time to heal so I have been a bit wary about throwing myself in to it and the manager has agreed with me," the striker said.
"But I have built up my substitute appearances and I have played reserve games.
"Of course I want to play but when he does call on me I will be ready to work hard.
"The most important thing is the club and it staying in the league."
Fulham have a reputation for struggling on their travels, but they have picked up four points on the road so far this term.
Martin Jol's side have coped admirably since losing Clint Dempsey and Mousa Dembele to Tottenham, and Roberts expects a tight encounter.
"Fulham at home is an opportunity for us," Roberts added.
"But they are a good side and I'm pretty sure they will come here thinking it is a good opportunity for themselves."