Swansea booked their place in next month's Capital One Cup final when they wrapped up a 2-0 aggregate win over European champions Chelsea.
The Swans were huge outsiders for a League Cup triumph at the start of the season, but their opponents Bradford were priced at a remarkable 2000-1 to lift the trophy.
Although Reading have experienced an upturn in form of late, they are still not fancied to reach their first FA Cup final this term.
But having watched Swansea and Bradford eliminate such heavyweights as Arsenal, Aston Villa, and Chelsea between them in the League Cup, McDermott hopes his team can carve out a route to the FA Cup final - starting with Saturday's fourth round clash against Sheffield United.
"What has been happening in the Capital One Cup with Swansea and Bradford gives us all hope," the Reading boss told a press conference.
"It's a fantastic story. You get one chance on the day and it's a one off.
"I texted Parky (Bradford manager Phil Parkinson) the other day and I might go there to support him in the final, he's a good friend of mine.
"It's amazing what he has done - the same for (Swansea boss) Michael Laudrup. At the moment it looks like he is going to be the manager of the year, he's done a fantastic job."