Jayawardene, speaking on the eve of the hosts' World Twenty20 opener against Zimbabwe, said it was tribute to Sri Lanka that they had reached three global title matches since winning the 1996 one-day World Cup.
"Lot of people have asked us why we have choked in the finals," he said. "I'd rather be in that situation than be knocked out in earlier rounds. So that means we are doing something pretty good in these big tournaments and we hope to continue that in World Twenty20."
Sri Lanka lost to Australia and then India in the 2007 and 2011 World Cup finals, and missed out on the World Twenty20 title when they were beaten by Pakistan in the 2009 final.
Jayawardene conceded that home expectations were now sky-high that Sri Lanka were now about to end their 16-year hunt for a second world title, with the benefit of home advantage and a balanced team.
"We are one of the favourites but we are part of the pack that, you know, if we get into a good momentum we could go all the way. We cannot put the hype down in the sense that we are playing at home," he said.
"Sri Lanka is a cricket-crazy country and the expectations would be high. People would back us so we need to enjoy that," Jayawardene added.
And he warned that Zimbabwe, who upset Australia at the inaugural World Twenty20 in 2007, needed to be taken seriously in today's curtain-raiser in Hambantota.
"They are a good team and can be attacking and very competitive," Jayawardene said. "We need to be at our best and not get complacent."
Sri Lanka's all-round skills in batting and bowling, with the spinner Ajantha Mendis back after a long injury lay-off, make them strong favourites today.
Zimbabwe have lost their last 12 official Twenty20 internationals, plus the two warm-up matches against Ireland and Bangladesh. But their captain Brendan Taylor was the star in the 2007 win over Australia when he hit an unbeaten half-century.
Despite his team's poor recent form, Taylor was upbeat.
"It's a tournament that we've probably had more success in than the one-day format or the few Tests that we have played," Taylor said. "It can be a bit unpredictable, does become tougher but we're a side that has developed really well and we are excited about playing. Hopefully we can spring a surprise."
Meanwhile, Kamran Akmal smashed an unbeaten 92 off 50 balls as Pakistan came from behind to defeat India by five wickets in a World Twenty20 warm-up match today.
Pakistan, chasing India’s commanding 185 for three, appeared to be out of contention when they lost five wickets by the 12th over with just 91 runs on the board at the R Premadasa Stadium.
But Kamran and the former captain Shoaib Malik turned the game around with an unbroken stand of 95 off 46 balls that helped Pakistan beat the shell-shocked Indians with five balls to spare.
Kamran plundered six sixes, including the winning shot off the seamer Irfan Pathan, which sailed over the cover fence. Malik remained unbeaten on 37.
Virat Kohli had earlier top-scored for India with 75 not out, while the off-spinner Ravichandran Ashwin claimed four wickets for 23 runs.
“We knew that if India could post a huge total, so could we,” Mohammad Hafeez, the Pakistan captain, said. “Kamran was exceptional, and Malik’s experience also helped.”
MS Dhoni, the India captain, said the batting worked well, but the bowlers needed to contain runs on the easy-paced wickets.
“It was not really a bad game for us,” he said. “We have got to work on a few things with our bowling.”
In other matches, England beat Australia by nine runs, Ireland pipped Bangladesh by five runs, the West Indies slammed Afghanistan by eight wickets and South Africa overcame New Zealand by nine runs.
England, the reigning champions, piled up 172 for six after being sent in to bat, the opener Alex Hales top-scoring with 52. Australia managed only 163 for six in reply against the tight England bowling despite a polished 71 from Michael Hussey, who hit five sixes.
England, who take on Afghanistan in their opening match in Colombo on Friday, play another warm-up match against Pakistan tomorrow.
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