The Lions' performance was highlighted by an outstanding try from George North but there were plenty of nervous moments, with Beale missing two penalty kicks in the final few minutes as the Lions clung to a two-point lead.
"That was entertaining, that's for sure," Warburton said on Sky Sports 1. "It was too close for comfort and the last 20 minutes were really hard. You have to give it to Australia, they went all the way and we'll expect a lot more in the next two Test matches. It's half a job done."
Hearts were in mouths when Beale lined up a penalty from long range in the dying seconds, but he slipped as he kicked and the ball fell short of its target as Lions celebrations began.
"It was like with Wales all over again," said Warburton. "It's out of your control when there's a kick to the other team in the last minute.
"There's massive delight to get the first win and get some momentum, and to get the ball rolling.
"We'll look forward to next week now."
Australia struck first with Israel Folau crossing the line after a superb move from Will Genia but the Lions kept plugging away and the kicking of Leigh Halfpenny before North's moment of brilliance put them on top.
"They came out very well in the first 20 minutes which is what we expected," Warburton said.
"It was a very quick first 20 minutes but we weathered the storm and put points on the board, and then it was to and fro. The sides are pretty even and that showed there as it went down to the last 10 seconds."
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- George North