Australia's narrow victory in last weekend's second Test means that the series is finely poised at 1-1 going into the final match, with the Lions on the verge of their first series victory since 1997.
Many had expected the vastly-experienced O'Driscoll to captain the side following an injury to tour skipper Sam Warburton, but instead he was left out of the squad, much to the bemusement of McBride.
"I was absolutely gutted. The first thing that came into my mind was that [Robbie] Deans, the Australian coach, must be laughing all the way," said McBride.
"The Australian media and others, Eddie Jones the previous Australian coach, have convinced them to drop O'Driscoll which I find amazing. He was the guy I would have tipped as captain of the tour. He has been a big influence so far. You live and die by the team you pick and we will see what Saturday brings.
"Brian O'Driscoll has been the greatest player we have ever produced in Ireland and I still think he is a major influence in any team."
O'Driscoll has been on four tours with the Lions, playing in eight Tests and scoring one try.