Murray sparked controversy in his new book when he claimed Lucas had staged a dressing room revolt moments before the Socceroos played Germany at the 2010 World Cup.
He claimed Neill had asked Verbeek to leave before scrubbing the whiteboard and telling players to forget the Dutchman's "bullshit" tactics and play their own game.
The alleged delay to going out on the pitch almost caused Australia to forfeit the game, said Murray, with the referee having to hurry them into the tunnel.
The match then ended in disaster, with Australia going down to ten men and being thrashed 4-0 by the dominant Germans.
However the claims sparked a furious backlash from Socceroo and Lucas Neill himself, who called the allegations 'scandalous' and threatened legal action.
Today Murray admitted his sources had got it wrong.
“In the light of new information that has come to hand I accept that I was misled by my sources and that Lucas Neill did not call for the team to ignore the then national coach’s instructions," he said in a statement.
“In my view Lucas Neill has been an outstanding captain of the Australian national football team and the third party report of the Australian game against Germany was never meant to be
disparaging of Mr Neill’s character and sense of duty to the team.
“I take this opportunity to unreservedly apologise to Lucas Neill for any hurt or embarrassment concerning this matter.”
He also promised that all reprints and new editions of his book will exclude this reference to Lucas Neill.
Today Neill accepted the apology and added: “I am obviously still disappointed that my name has been wrongly attached to these allegations.
"But I accept the apology that has been issued by Les Murray."
He added: “After discussing the matter with Les, I have decided not to proceed with legal
"It was important for me to ensure that my reputation remain intact and make the public aware that I have never, nor would ever, behave in this manner towards a manager.
"Furthermore I’m happy that any further prints of the book will exclude this extract. I sincerely hope that anybody who reads the book in its current form understands that the allegations that were reported about me are completely false.”