However, the 34-year-old was instead dropped by head coach Warren Gatland as he made six changes to his side for the match in Sydney, a choice labelled a "terrible mistake" by ex-Lions hooker Keith Wood.
Without O'Driscoll - who has also captained the Lions in six other tour games - McGeechan urged stand-in skipper Alun Wyn Jones and fly-half Jonathan Sexton to shoulder responsibility.
"Alan Wyn Jones will have to have his moments when he pulls the players together on the field," McGeechan told the BBC's chief sports correspondent Dan Roan.
"As a coach, you can be sending messages on, but you need those moments when everybody is together.
"He will have to take responsibility for that. Jonny Sexton has a big responsibility as well to play the game in the right areas, and if necessary, make some big calls and have some confidence to do that."
30 October 1946
Despite being born in Leeds, played at fly-half or centre for Scotland. Also selected for the 1974 and 1977 Lions tours.
Lions coaching career:
Has been head coach of the Lions on four occasions, gaining series victories in 1989 and 1997. Also guided the midweek side in 2005.
"I would have liked to have seen him playing with Jamie Roberts because they were such a good partnership in 2009," said McGeechan, who was head coach for the Lions on the 1989, 1993, 1997 and 2009 tours.
"They do understand each other, they have a very good chemistry, and with 80 minutes to win a Test series that combination could have given us some special moments."
McGeechan was in charge the last time the Lions won a Test series, when they triumphed in South Africa 16 years ago, and he believes Saturday's match at Sydney's ANZ Stadium is the tourists' most important game since that victory.
"For the Lions and what they stand for, it is the biggest game since 1997," he said.
"There is a Test series to win, and from our perspective, that is very important."
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