The Royals remain rooted to the bottom of the Barclays 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."