Beale had come on as a replacement for Berrick Barnes and showed his undoubted class during a see-saw second half.
And when the Lions were penalised 45 metres out, he had the chance to give the Wallabies the advantage in the three-match series.
He slipped on his approach to the ball though and with the kick going wide, it meant the Lions hung on for victory.
"It's out of your control when there's a kick to the other team in the last minute," Warburton told Sky Sports immediately after the win.
"We gave away cheap penalties so there's plenty to work on but it's such a massive achievement to come out here and get the win."
Both sides scored two tries apiece in Brisbane, Israel Folau crossing for a brace on his Australian debut.
But missed kicks from Beale and fly half James O'Connor proved decisive as Robbie Deans' men slipped to defeat.
"That was entertaining, that's for sure," Warburton said when summing up the game.
"You have to give credit to Australia and we'll expect more in the next two Test matches. It's half a job done."
"We probably played a bit too much rugby in our own half but we've won the first Test and I'm really happy with the result," added Lions head coach Warren Gatland.
"Next week we will have a few players back and that will strengthen our squad. It wasn't the prettiest performance, but it was the victory we deserved."