"We are looking forward to another tough match in the semi-final," Jayawardene, who was adjudged the Ma of the Match for his unbeaten 84, said.
A disciplined Sri Lanka set up a semifinal date with India as they knocked out holders Australia, with Jayawardene and Nuwan Kulasekara playing key roles.
During the course of his innings, the elegant Jayawardene crossed 11,000 runs in this form of the game.
"That has been the mantra of our success in the past and hope it continues in the future. Seniors have a responsibility and it is our job to help Angi (skipper Angelo Mathews) out, that makes us a happy camp," Jayawardene said.
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After setting a target of 254, Mathews said he knew it was going to be tough as Australia managed 233 before being bowled out.
"We knew it was going to be tough, defending 253," said Mathews.
Australia's stand-in skipper George Bailey felt his side never got going.
"It would have been nice to get over the line in the end. Our goal was to do it in the 29 overs, but we never got going. There was no value in the result as such, semis was our main aim," Bailey said.