McGinley got the nod at the European Tour tournament committee meeting in Abu Dhabi, the Dubliner seeing off Scots trio Montgomerie, Paul Lawrie and Sandy Lyle, and Spain's Miguel Angel Jimenez to land the coveted position.
But Monty, who led Europe to victory in Wales three years ago and became a late contender for the job after Tom Watson was put in charge of the Americans, said: "I'm not at all disappointed – it would have been a dream come true, but it has not happened.
"I was very flattered even to be considered again – it meant a lot to me. The selection process was such that they appointed the best man for the job.
"We all get behind Paul now and wish him well. I appointed him for the Seve Trophy and he did a very good job – as he did twice as a vice-captain (in the Ryder Cup). He's a very good man-manager and very good at assessing people's strengths. I will be there to support and fly the flag for Europe."
Montgomerie lives only a few miles from Gleneagles and is bound to be on the list of possible assistant captains for the match in September next year. Asked if he had any bitterness about the way things turned out, the 49-year-old said: "Goodness no. It's nothing to do with that."
As for whether he might ever again be in the running for the job, Monty added: "Only if we keep losing and I do a Tom Watson and come back!"
McGinley paid tribute to Montgomerie and revealed the Scot had been quick to congratulate him on his appointment.
"He was the first man I saw, he came up and congratulated me warmly and wished me the very best of luck," he said. "He was very, very gracious to me."
He added: "Monty has been a great captain and a great stalwart of Ryder Cups. I have played in three Ryder cups with Monty, everybody knows what the Ryder Cup means to him and how he has carried the Ryder Cup, not just as a player, but how he spoke at the meetings and the air of authority he had around it."