The tourists created a bit of history, when they completed a 121-run victory over Chris Gayle's side in the opening Test on Wednesday.
"We had a challenge when we came and that was to win a Test match in the West Indies and we have achieved that," Jayawardene told reporters.
"We played hard and a lot of guys contributed. It was an amazing effort from Chaminda Vaas, and our 'quicks' took 13 wickets in the Test, so a lot of credit to them.
Muttiah Muralitharan bowled his heart out, and overall it was a very good team effort.
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Jayawardene felt West Indies played into his side's hands, when they chose to chase an unlikely 437 to win.
"We wanted them to play a few shots on this pitch because that's how we could have created opportunities," he said.
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"That's why we gave them a target they could have achieved, rather than giving them 500 when they would have been in a very defensive frame of mind. We gave them a target thinking this is a target they could chase especially since they