"We will go there with our heads up," O'Driscoll, who was one of the Lions' star performers last weekend, said in his column in the Guardian.
"The character of a side is often determined in the way it bounces back from defeat. We are bitterly disappointed, but not as much as we would have been had we been outplayed.
"The fact that we created opportunities throughout will sustain us in the coming days - the Springboks may have won a battle, but the war is another matter."
O'Driscoll set up two tries for flanker Tom Croft at the ABSA Stadium and was a consistent thorn in the Springbok side. His blossoming centre partnership with Welshman Jamie Roberts created numerous opportunities for the tourists, while the Boks themselves had very little joy when they targeted the Lions' midfield.
The Ireland skipper has now played in five Tests for the Lions, winning only once on his first outing in Lions colours back in 2001.
On that tour it was the Lions who blew the Wallabies out of the water in the opening half of the first Test, only to allow Australia back into the game in the latter stages. The Wallabies recovered from 1-0 down to win the series 2-1 eight years ago and O'Driscoll would love to see the Lions match that feat this time around.
"We dominated the game in terms of territory, we took play through far more phases than South Africa and we made a number of line breaks. But we were punished for our mistakes and problems at the scrum in the first half," added O'Driscoll.
"This series is far from over, but we cannot afford to make the same mistakes and we have to be more clinical close to their line, finishing off what we start. It is all there and we have no reason to panic.
"We have to ensure at Loftus Versfeld that we start better. They will be better for having played their first game in seven months but we have to up the intensity and not give them a head start.
"They may have won the opening Test, but they will be only too aware that it came down to a couple of video-referee decisions and a ball dropped on the line.
"An international match invariably comes down to small margins and we had the chances to win. It is no use asking whether the referee was right or wrong in the key decisions he made, because the game has gone.
"It is now all about Pretoria, moving on and absorbing the lessons from Durban."