The Royals remain rooted to the bottom of the Premier League as the season approaches its mid-point after losing their last seven matches.
But after going down 5-2 to Arsenal last week, McDermott's men at least responded strongly with a creditable performance at Manchester City on Saturday.
Reading were just moments away from a much-needed and morale-boosting point when Gareth Barry headed an injury-time winner for the champions at the Etihad Stadium.
McDermott now wants to build some momentum from that display and has called on the supporters to play their part as Swansea visit the Madejski Stadium on Boxing Day.
McDermott, who is under pressure despite his acclaimed role in last season's promotion, said: "In the last three games we haven't really performed the way I know we can.
"But against Arsenal we were three and four down and we fought back.
"You could see the spirit in the group and you certainly saw the spirit in the group on Saturday.
"You respond by trying to win the next two games. We have got Swansea at home and West Ham at home.
"We need our fans massively to be with us. They took so much credit from last year, dragging us over the line. We need them to be with us again."
McDermott's position has come under scrutiny during his team's poor run but the 51-year-old has brushed aside speculation over his future.
The former Arsenal player earned widespread plaudits by guiding his side out of the Championship and his ambitions have not diminished.
He said: "It is hard at the moment, sat here after losing a goal at Man City, late like that.
"It really is difficult and it is tough to take but you have to.
"One thing I have found out about myself in the last three years is I am resilient person and you have to be in this job."
Swansea will travel to Berkshire confident after securing another impressive result by holding leaders Manchester United to a draw on Sunday.
The Welsh side are just six points off fourth place but Reading led 2-0 against them in October before being pegged back for a draw.
McDermott said: "I know Swansea are a good side. We were 2-0 up against them at the Liberty Stadium.
"We are looking forward to a full house at the Madejski Stadium on Boxing Day."
Veteran striker Jason Roberts is nearing fitness but not yet ready to return after a fortnight out with a hip injury.
Defender Sean Morrison is also still troubled by an ankle problem and goalkeeper Alex McCarthy is out long-term after a shoulder operation but McDermott is pleased his injury list is otherwise easing.
He said: "Lads are coming back. We saw Jem Karacan on Saturday and Danny Guthrie was back.
"Jimmy Kebe out in one hell of a shift and did really well.
"Jason Roberts - not quite yet, and Alex McCarthy, obviously long term, but we are getting the players back, which is important to us."
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