Crawley, who had reached the fifth round in each of the last two seasons, made the perfect start at the Broadfield Stadium with Nicky Adams' 25-yard strike.
"It was about coming and trying to get a result and do the basics as well as we could, which we didn't in the first 14 seconds," McDermott said with a wry smile.
"They had another chance to go 2-0 up, which would have been a real problem. It is easy to panic but we got ourselves back into the game. The reaction from our players was good.
"When we got ourselves 2-1 up it was more comfortable for us. I thought the combination of Adam and Noel was really good and Garath McCleary made a really good goal for Noel.
"We made a few changes but we put out a team we thought could win and that is what happened.
"It has turned out to be an okay day. I am pleased to be in the next round."