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.
McDermott said: "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?
"But we played some great football after that and that gives me real hope going forward."
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."
McDermott also felt his side should have had a penalty in the second half after Sylvain Distin appeared to handle an Adam Le Fondre cross.
He said: "He put his hand up and nearly caught it, but he didn't (catch it) so he (the ref) didn't see it. It was a penalty I thought."
Goalkeeper Adam Federici missed the trip to Merseyside after being hurt in training while winger Jimmy Kebe pulled up in the first half.
McDermott said: "Adam went down in a training session yesterday [Friday], did his ankle.
"It's not fractured and we're hoping it's just sprained. We'll wait and see.
"Jimmy came off with a groin strain and we don't know how bad that is yet."
Victory kept Everton in the picture for Champions League qualification.
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.
Moyes felt unable to comment much on another incident involving Reading's Noel Hunt and Jagielka's replacement John Heitinga.
Moyes said: "I haven't seen that one but I will have a look at it. I was surprised the referee didn't stop play.
"If he didn't see it you might hope one of his two officials might have spotted it."
Moyes was pleased with the performance of Fellaini on his return from a knee injury and was happy to see Pienaar among the goals after a superb long-range strike from the South African.
The Scot said: "Fellaini came back and was an influence. Seamus Coleman put over a brilliant cross for him for his goal and had put in a couple of good crosses prior to that.
"He has got a lot of really good attributes. He can get better but he has got a lot going for him. On his day he can be a handful.
"It was a great goal from Steven. I am pleased for him, he is an important player.
"One of the things that can be labelled at him is that he probably doesn't score enough.
"He is beginning to get a few goals and today's [Saturday's] was right out of the sweet spot and that was good."