The midfielder's decisive strike earned a 2-1 win over last season's beaten play-off semi-finalists, sending the majority of a sold-out Elland Road into delirium on a day which had been heralded as the first of a new era at the club.
With controversial former chairman Ken Bates having been ousted over the summer, it was perhaps fitting for the home fans that their first million-pound player in eight years won the day.
Bates was often accused of failing to splash the cash but former Crewe man Murphy paid off some of his fee with the goal, even if there was a hint of handball about it as he took in a Matt Smith flick.
"I think it connected with his hand. Whether it was handball or not, I don't know," McDermott said with a knowing smile.
"There was a dispute, but there was about their goal which was a yard offside. Then we get a goal with the last kick of the game and you take that on the first day of the season.
"Both sides could have won no doubt but in the Championship if you try and win and keep going, you get the breaks."
The breaks McDermott referred to were Murphy's 'handball' and a string of fine saves from Paddy Kenny which kept Brighton at bay.
Andrew Crofts - who supplied Leonardo Ulloa's opener - was one man denied, along with Inigo Calderon and Will Buckley.
"Paddy made a match-winning save twice and when you do that, you hope you get the break at the other end," McDermott added.
"I think we deserved a break and we got one. We could have had a penalty and didn't, their goal was offside and then we scored."
On Murphy, his solo paid-for signing since taking over, he said: "He scored a great goal at Wembley for Crewe and if you can play at that stadium, at 23 years of age, you're ready."
The late drama gave Brighton coach Oscar Garcia a harsh welcome to English football, having swapped Maccabi Tel Aviv for Sussex over the summer.
The Spaniard insisted on taking the defeat with good grace, though.
"I couldn't see it, everybody said yes, it was handball, but to be a referee is very difficult and I can understand if he did not see a handball," he said.
"It is more disappointing when we had a chance to score five minutes before.
"Leeds are a physical team and more so when they play at home so we knew it would be tough. We had our chances and did not take them, so we got this result."
Unlike his often-emotional predecessor, Gus Poyet, the former Barcelona midfielder was relatively sedate throughout the game, even though his men let Ulloa's goal mean nothing as Ross McCormack and then Murphy scored.
He indicated he does have a harsher side, though, saying: "Tomorrow the players will know what I think of the performance. I am only happy when we play 100 per cent."