The Magpies head coach hit out at the official for not awarding his side a penalty and then pointing to the spot at the other end and sending off skipper Fabricio Coloccini as the Black Cats broke in an explosive conclusion to the first half at the Stadium of Light.
Sunderland took full advantage of what manager Sam Allardyce later admitted had been a stroke of good fortune to run out 3-0 winners and claim their first Barclays Premier League victory of the campaign at the 10th attempt.
McClaren said: "I don't think frustrated is the word - angry, disappointed... Two decisions have cost us a game in which we were totally dominant, looked a very good side, frustrated the crowd - it was a perfect performance in the first half."
Newcastle went into first-half stoppage time having bossed the game, but crucially without having made it tell, and they were stung in devastating style twice within seconds.
Midfielder Georginio Wijnaldum was left appealing in vain for a penalty after Lee Cattermole appeared to handle the ball inside the box and then haul him to the ground with referee Madley unmoved.
However, he had no hesitation in pointing to the spot at the other end seconds later after Coloccini leaned rather too heavily on Steven Fletcher as he tried to shepherd the ball back to goalkeeper Rob Elliot, rubbing salt into the wound by also producing a red card.
McClaren said: "It's simple: he is wrong in my opinion. Referees are part and parcel of the game and you control your performance - you can't control the opponent or the referee and they can affect the result. And they have done today - not so much the opponent, but definitely the referee.
"I have seen lots of challenges like that in the game, in every game and, outside the box, they are never given. It's a double whammy - a penalty and 10 men. It made it very difficult.
"We need an experienced referee for this and I think in both instances, he was a little too quick to make a decision."