The Royals were close to securing their first win in the Barclays Premier League this season when they led Newcastle 2-1 last weekend.
But their hopes were dashed when Demba Ba grabbed a dramatic 83rd-minute equaliser, although the Senegal striker clearly diverted the ball into the net using his arm.
McDermott was unhappy with the decision and was left perplexed when the fourth official suggested a more vehement appeal from his players could have seen the goal chalked off.
"I feel a sense of injustice because there was an injustice - obviously the goal shouldn't have stood," he said.
"My concern slightly, or more than slightly, is the conversations with two people now; the match delegate at the Chelsea game said that my players didn't appeal for the (Fernando) Torres offside goal, and the fourth official said to my goalkeeping coach that only two of my players appealed (against Newcastle).
"For me it is very difficult to take that, what are we asking? If we appeal for every decision we might get one or two?
"The last thing we want is for our players to start trying to referee the game, we have to let the referee and the assistant referees get on with their job and that is what we are trying to do.
"So that is the concern for me, the two separate things that have been said to me."
McDermott, 51, has also backed his players to always act in an appropriate manner on the pitch, citing the club's £40,000 fine and Football Association warning for failure to control their players during a 2-2 draw with Cardiff in 2011 as a lesson learned.
"Since we had that incident against Cardiff our players have been absolutely impeccable," he said.
"What went on there a couple of years ago at Cardiff is history, our players have been impeccable. I'm proud of their discipline and everything they do and the way they go about their business.
"We have to do what we have to do and obviously with the officials we let them get on with their job."
Reading travel to Swansea on Saturday still in search of their maiden league win this season.
McDermott's side suffered a 4-2 defeat to the Swans in the 2011 play-off final but does not see the trip to the Liberty Stadium as a grudge match for his players.
When asked if he was seeking revenge at Swansea, McDermott said: "No, not at all it is a game of football.
"I'm not into revenge, it is a game of football which on the day we lost, Swansea won the game and history is history.
"We have moved on and Swansea have done fantastically well in the league last year, we are in the Barclays Premier League so we have done what we had to do.
"The time wasn't right for us then, it was right for us last season so there is not even a thought of that in my mind, all we are trying to do is go there and put in the right performance."
Ex-Reading boss Brendan Rodgers guided Swansea to success that day but has since left the club and been replaced by Michael Laudrup, someone who McDermott has great respect for.
"I've seen a couple of the games they have been involved in and I like the manager there," he said.
"Everybody knows this guy in the world I'd say, in the meeting we had recently of the Premier League managers he came up and said 'hello Brian, its Michael Laudrup' and I thought 'I know that'.
"But it was really respectful and it says something about the man really, he seems a humble man and I really like him."