A deflected first-half free-kick from defender Ian Harte proved enough to give Reading maximum points at the Amex as Brighton went down to their first home league defeat in nearly four months.
"It was a night of resilience and character," McDermott said. "Brighton are a difficult side to play against, they had a lot of the ball and we had to hang in there."
Reading now boast 12 away wins - more than any other side in the npower Championship - and McDermott is targeting another victory on the road against leaders Southampton at St Mary's on Friday.
The Royals are only behind Southampton on goal difference, and McDermott added: "We have followed up a hard-fought win over Leeds with another win and all I'm thinking about now is the Southampton game.
"St Mary's will be the place to be on Friday, I'm sure."
The defeat ended a run of 10 unbeaten home league games for Brighton, and McDermott believes the Seagulls will provide a real test should they squeeze into the play-offs.
"Brighton are a good side, they pass the ball very well and make the pitch big," he said. "If they get themselves into the play-offs they will be a tough side to play against."
Brighton manager Gus Poyet took consolation from his side's defeat by the manner of their performance and predicted the Seagulls would come back stronger next season even if they miss out on the play-offs.
"I take huge encouragement from this performance," he said. "If we keep the same players fit and if we add some more key, important players, us going to the Premier League will just be a matter of time."