USA captain Fred Couples opted to include Woods as a captain's pick several weeks before final selections had to be made.
"You can't ever say that picking Tiger Woods is a bad selection, but the way he picked him," Ogilvy said.
"I don't agree with the way he picked him, announcing it months early, basically telling the guys who are on the fringe of the US team there's really only going to be one pick.
"I'm not going to stand up and say Tiger is a horrible pick, but I'm going to say it's very disappointing that Keegan Bradley doesn't get to play."
USA take on a Rest of the World team in the Presidents Cup at the Royal Melbourne Golf Club in Australia.
The tournament gets underway on Thursday, November 17.