Australia v Lions: Warren Gatland blames 'critical turnovers'
"Of course I want to lead the team in the third Test and I'll do everything I can to do that."
Warburton watched from the sidelines as Wallabies centre Christian Leali'ifano converted Adam Ashley-Cooper's late try to level the series.
In a dramatic finish, Leigh Halfpenny had the chance to snatch victory for the Lions with the last kick of the game, but his penalty from halfway fell short.
Lions head coach Warren Gatland felt Warburton's injury impacted on his side during the closing stages at the Etihad Stadium.
"I thought Sam was brilliant at the breakdown, particularly in the first half, when we had a number of turnovers. I think that was the difference between the two sides," Gatland said.
"It was a big loss when he came off. Dan Lydiate had run himself into the ground and we probably would have brought Dan off and Tom Croft on for him.
"Unfortunately Sam has picked up that injury which has perhaps changed the momentum a bit."
Warburton was in defiant mood despite the loss and is confident the tourists can bounce back and win the series in Sydney.
"We're going through what Australia went through last week," Warburton said.
"It's disappointing now, but I think the boys will wake up tomorrow and realise that we've still got a Test series up for grabs. And we've got every chance of doing that.
"We have to pick ourselves back up now, and there's some good stuff in there.
"We're definitely capable of taking the Test series, we've shown that for two games. It's going to be won be a whisker next week, and I hope it's us."