The Lions led by 11 points with 20 minutes remaining at Loftus Versfeld in Pretoria, and having fought back to within inches of victory in the first Test, McGeechan insisted: "We could be sat here with two Test victories.
"We haven't had the rub of the green on the field. The effort that has been put in by the players has been phenomenal."
The Lions suffered a host of injuries in Pretoria, including losing first-choice props Gethin Jenkins and Adam Jones, but McGeechan is confident his battered team can still win the final Test.
"There's a lot of character in this group," he said. "People asked me the same question last week and I think they got their answer. It will be the same again.
"They're an incredible group of young men. Whatever happens with injuries, we'll be ready to win the third Test."
Victorious Springbok captain John Smit described the second Test as "a game of two halves" after the world champions fought back to win having been outplayed for the first 40 minutes.
Smit hails 'colossal' Test match
Twelve years ago the Lions won after some poor goal-kicking from the hosts and Smit said it was "ironic" that a superb penalty should secure the 2009 series for the Boks after Jeremy Guscott's drop-goal clinched the series for the Lions in 1997.
"When he (Morne Steyn) cracked that ball I was pretty happy," said the captain.
"I'm proud of the boys. I knew the intensity and physicality was going be tougher than last week.
"We were hard on each other at half-time, some honest words were spoken, but this team keeps amazing me.
"It was wonderful Test match. There was a contest in every area of the pitch. The job is done and now it's time to enjoy this win."
Lions captain Paul O'Connell described the result as "very disappointing".
"We had a lot of injuries and I suppose they told," he added. "It was tough but we just didn't play enough in the second half. We were all over them when we played in the first half.
"The commitment was incredible, all the lads are so proud and want to win for the Lions."
English second row Simon Shaw was named man of the match after a storming display as he became, at the age of 35, the oldest Lions Test debutant in history.
He said: "It's devastating to have lost in that fashion.
"Geech (McGeechan) has said we should be proud of ourselves but ultimately we've lost the series and it's difficult to lift anyone right now.
"I was hoping it was going to be our day. I would rather been taken off at half-time having played poorly than have lost the game and won man of the match."
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