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.
Swansea visit the Madejski Stadium on Boxing Day, and McDermott 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."
He continued: "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."
Source: PA
Source: PA