Sri Lanka, the champions in 2014, play their final Group D game on Sunday against the Netherlands after losing to Bangladesh and South Africa.
Their only point came from a washed-out no-result against Nepal.
"I think first of all we've let the entire nation down and we are really sorry because we've also let ourselves down," said former skipper Mathews.
"We never expected this. We came across a lot of challenges but those are not something to sort of worry about, but it's unfortunate that we didn't make the second round."
Mathews played a key role in his country's 2014 World Cup victory, scoring 40 runs in the semi-final against West Indies and taking 1-25 in the six-wicket win over India in the final at Dhaka.
Sri Lanka will have just pride at stake when they meet the Dutch on Sunday where a victory will at least help them climb off the foot of the table.
However, Mathews, who will be playing in his 90th T20 international, insists his team won't under-estimate the Netherlands having seen Nepal lose by just one run to South Africa on Friday.
"We can't take any given team lightly. It's unfortunate that our Nepal game was washed out but it is what it is," he said.
"We have just one more game in the tournament, and we'll play for our pride. We haven't done justice to ourselves, especially the way we played in the first two games.
"We are heartbroken and are hurting so much within ourselves."
