Shane Long's late strike earned the Royals a 2-1 win at the League Two side after Mikele Leigertwood had found the target for the first time since signing from QPR.
McDermott said: "I'm delighted we've got through, of course, but they have made us work so hard every step of the way.
"We thought we were in for a tricky final period when Stevenage equalised as they did with a great strike, but in the end I don't think anyone can begrudge us our victory.
"Let's see who we can take on in the last 16 now.
"We've had a couple of decent runs in the cup over the past few seasons. Maybe we can even make it past the quarter-finals this year."