It took a superb touchline penalty from Jonny Wilkinson eight minutes into stoppage time for the Lions to hold the South Americans.
"We were lucky to get away with the draw," said Wales star Owen, on familiar ground in the Millennium Stadium as the Lions played their final match before heading off on their summer trip to New Zealand.
Owen was skippering the side as newly-appointed Lions captain Brian O'Driscoll watched on from pitchside, with head coach Sir Clive Woodward opting to take advantage of his large squad for a match he has stressed represented the first of the tour.
"It was bitterly disappointing," said Owen, "but we've got to take the positives out of the game."
Owen conceded the Lions had performed below the standard required of a team hoping to give the All Blacks a run for their money.
"We were losing the ball and couldn't get our game going," he added.
"This happens in rugby. We have highs and we have lows. This isn't a low, it's a disappointment, but we have to fight back."
Wilkinson told Sky Sports 1 that, on his first international since kicking England to World Cup glory in November 2003, the daunting kick to save the game was one he would rather have not needed to make.
"I wasn't hoping for one of those," he said.
"We'll take the positives but we're glad to see the negatives and we'll go away and work on them."
He added: "I think there were glimpses [of quality] there.
"We did lose the ball a bit and you can't play rugby when you're losing the ball.
"It could have been a different story if we hadn't pulled together and come out of it."