Sri Lanka collapsed after their mainstay Kumar Sangakkara was sensationally given out cheaply in their second innings by the review system when a draw, and possibly a remarkable series levelling win, were still possible.
After Sangakkara had moved to one behind the legendary Don Bradman for the most double centuries with his 203 in the first innings, Sri Lanka had a comfortable 135-run lead.
Victory seemed a formality when they had New Zealand at 159-5 in their second innings, a mere 24 runs ahead with more than two days to play.
But sloppy fielding allowed New Zealand to total 524-5, with four chances wasted to remove Kane Williamson who went on to make an unbeaten 242 after first being dropped on 29.
Facing a tough but not improbable target of 390 to win, Sri Lanka reached 61-2 when Sangakkara was dismissed for five in the morning session of the last day and the rest of the batting limply folded.
"It was a shocking turnaround," Mathews responded when questioned why Sri Lanka lost a game they had in control.
The first problem was the fielding and the succession of lives afforded Williamson.
"If we had held on to our catches, it would have been a different story. But they were able to reverse the pressure on us and we just couldn't hold on," he said.
"You can't really drop those sitters when you're on the way to winning the game and you are desperate to win the game."
But the main calamity came when a flyer from New Zealand quick Trent Boult flew past Sangakkara when Sri Lanka were 61-2 in the second innings.
Boult gave a half-hearted appeal, wicketkeeper BJ Watling seemed disinterested, but with nothing to lose New Zealand captain Brendon McCullum thought it was worth seeking a review.
After countless inconclusive replays, third umpire Bruce Oxenford suspected there was enough sound and touch that the ball had feathered the bat and Sangakkara was on his way.
"Umpires have a tough job at hand and you can't really comment (on the review system). You have to be careful with that," Mathews said.
"That's the way it goes and unfortunately, or fortunately, we have to take it as it comes."
Despite the controversial dismissal, Mathews felt he was let down by the lack of fight from the remainder of his batting line up as the last eight wickets fell for 135 runs.
"He was the man in form and we needed somebody to bat through the innings and Sanga's wicket was the crucial one," he said.
"We had to build up partnerships around him but I think we shouldn't put a lot of pressure on him. He is a world class player and one of the best we have seen, but we also need the youngsters to grab hold of their opportunities and score some runs.
"Slowly but surely the youngsters will learn but this is international cricket and we can't expect one person to score all the time so we need to grab hold of our opportunities and try and be consistent."
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