The Royals are six points short of the top six with 12 games remaining and McDermott believes they have the quality to challenge.
He said: "We have drawn 15 games this season.
"If we had won just a few more of those you never know where we could have ended up.
"The Liverpool win last year gave us impetus and we can take the same confidence from playing with quality at Everton.
"If we can do that between now and the end of the season we stand a chance."
Source: PA
Source: PA