The Royals slumped to a 3-1 loss at Goodison Park to remain in the bottom three of the Barclays Premier League, but the visitors hit the woodwork with the score still 0-0 and had other opportunities before Marouane Fellaini struck after 43 minutes and Everton then eased away with further Steven Pienaar and Kevin Mirallas strikes.
Reading battled on and grabbed a late equaliser through substitute Hal Robson-Kanu, and McDermott said: "We played some great football after that and that gives me real hope going forward."
He added: "There was nothing in the first half but they have got major quality. When Adam Le Fondre had a shot and hit the post - if that goes in maybe it's different. It was a great goal they scored, the first goal and the second goal, what can you say?"
McDermott's side have 10 games remaining to save their top-flight status and the manager hopes they can repeat the late-season charge which earned them promotion last term.
He said: "We had to make up about 14 points last year and we did that. We have to make up one or two at this time - we think we can do that. We have to keep doing our stuff, keep the spirit going and the group together.
"We have finished the last three seasons really strongly. If we can do the same this season I'll take that. It would give us a real chance. There is not a lot in the league at all really."
Manager David Moyes was pleased with the performance but felt it took time to build momentum after losing defender Phil Jagielka to injury in the opening minutes.
Moyes said: "We played well. I thought we started well but the injury rocked us badly and it took us a wee while to settle after that. Reading were always a threat, had a few chances, hit the bar. That is the way the Premier League is, whoever you play, the games are tight."
Jagielka could face a spell out after suffering a "bad, bad gash" in a challenge by Le Fondre.
Source: PA
Source: PA