Captain Matt Mills struck the only goal at Goodison Park to send the Royals into the quarterfinals.
McDermott said: "I was as bullish as I was ever going to be.
"I was looking forward to the game because it is just a great place to come and play.
"I felt that if we set our team up in the right manner and went about business in the right way, I knew we had players who could make a difference.
"You have to be disciplined when you come here - they passed it around for the first 20 minutes and did really well.
"But we did what we had to do and I thought we were deserved winners tonight."