McGinley's appointment on Tuesday as the first Irish skipper in the 86-year history of the event came at the end of a campaign during which golfing politics came to the fore.
Tour players came out in support of their own favorites in the newspapers and on social networking sites in the weeks leading up to the selection, causing a swirl of media debate about which of the candidates was most suited to the role.
"It was never meant to be a campaigning business," O'Grady told Reuters in an interview on the eve of the $2.7 million Abu Dhabi Championship.
"That will probably have to be looked at in the cold light of day but the world has changed with all this twittering.
"I think personally one person should be invited to become captain and there should be no losers. There should be a view that this is the right guy at the right time because it can all be a little unseemly."
Ten members of the 15-man Players Committee, chaired by Dane Thomas Bjorn, debated the respective merits of McGinley, 2010 skipper Colin Montgomerie, Miguel Angel Jimenez, Paul Lawrie and Sandy Lyle at a meeting in Abu Dhabi on Tuesday before plumping for the Irishman.
"In the end, with all the talk in the social media and the newspapers in the run-up, it was a triumph for democracy," added O'Grady.
"It was done very well. The decision was taken by the committee, it was a unanimous decision but it was more a consensus of everybody's feelings.
"I think to have a guy announced as captain and to have the world number one (Rory McIlroy) coming in at the back of the room to show his support gives you great confidence," said O'Grady.
Before the Players Committee meeting, McIlroy said he felt strongly that McGinley should be appointed and the twice major champion was there to back his man when the decision was announced to the world's media in a hotel conference room.
Bjorn said the captaincy never went to a vote and O'Grady congratulated the Dane for the way the meeting was conducted.
"We have to say the Players Committee have a habit of getting it right," said O'Grady. "Thomas chaired the meeting superbly well, everybody had their viewpoint, it went round the table once and then people had a view.
"No single player dominated at all, one person proposed Paul and the motion was carried.
"The actual physical process was conducted superbly but whether we need all that space in the papers, we'll think about that calmly," added O'Grady.
The tour chief backed McGinley's selection and said he would make an "outstanding captain".
"We can't be unaware of the fact that so many members of the current team were so supportive of Paul," he explained.
"Everyone in the room accepted the outstanding credentials of all the other candidates, especially Colin Montgomerie who was an outstanding captain in 2010, but generally speaking there's an unwritten rule that you do the job once (only)."
McGinley succeeds Spain's Jose Maria Olazabal who led Europe to a remarkable comeback victory over the United States in Illinois in the biennial team event in September.
O'Grady said the 46-year-old Dubliner would be his own man when the holders attempt to retain the trophy at Gleneagles, Scotland in 2014.
"I think he'll be meticulous, passionate, organized, aware of everything," said the European Tour chief. "He will have a consensus way of working with the players, like a general.
"He'll bring his own personal style, just like Olazabal has done and Montgomerie has done. It will be different but it'll be his way of doing it.
"He is a feet-on-the-ground merchant but if the starting point is the world number one and a few of the other players are on his side, then they are going to play mighty hard for him, I'd say."
(Editing by Amlan Chakraborty)