"The next two weeks for us is the showcase time for the whole tournament, and our senior players, who have been in World Cups before, I think that's when you'll see them stand up and start enjoying the tournament for what it is.
"
The reigning champions, chasing an unprecedented third successive title, have gone 25 games unbeaten at the World Cup since losing to Pakistan at Headingley eight years ago, a sequence that includes their famous tied semi-final against South Africa in 1999.
Australia's nine-wicket thrashing of Ireland on Friday was their 19th straight World Cup win and meant they became the first team in the Caribbean to qualify for the semi-finals.
New Zealand and Sri Lanka have also joined them in the last four courtesy of the Black Caps' win over South Africa on Saturday.
"I think we have a very good record against Australia," said Jayawardene.
"Why? Because we play our brand of cricket and we are not afraid of doing that.
"
But Sri Lanka will still be without Lasith Ma