Gatland caused a massive stir after controversially opting to omit the experienced Ireland centre as one of six changes to last weekend's 16-15 defeat to the Wallabies.
Carling, who toured with the Lions in 1993, said: "My jaw almost hit the floor when I heard the news. Gatland will be hung out to dry if he gets this one wrong and I firmly believe he has made the wrong call. There is just no logic to his decision. I would never pick a team on sentiment but O'Driscoll would still be in my team on merit."
He added: "Okay, he hasn't set the world alight in this Test series but in make-or-break games like this you need players of proven world class.
"O'Driscoll ticks all the boxes. And because of that I'd have given him the captaincy."
Carling is not the only former Lion to have criticised the decision to axe O'Driscoll, but Gatland has received a measure of support from England's World Cup-winning coach Sir Clive Woodward.
Woodward, who represented the Lions as a player in 1980 and 1983 and as coach in 2005, believes Gatland was right to leave O'Driscoll out of his starting line-up, although he believes the Irishman should have been on the bench.
"A head coach cannot afford to be sentimental," said Woodward, who appointed O'Driscoll as his Lions captain in 2005.
"Dropping Brian O'Driscoll is the right decision based on his form and the way the Lions need to play to win this series."
He added in his column in the Daily Mail: "I agree with dropping O'Driscoll from the team, but he should not have been left out of the match-day squad. I would much rather have the 125 caps and game-changing intelligence of O'Driscoll to call upon in the final 20 minutes of a must-win Test than the inexperience of Manu Tuilagi."