But he said whether the 'brilliant' coach stayed with the side beyond the World Cup was a matter for the former Australia international alone.
Moody, twice a World Cup winner as a player, has been tipped to succeed Duncan Fletcher as England coach following the side's 5-0 Ashes thrashing by Australia, and has said he will review his future after the World Cup.
Formerly in charge of English county Worcestershire, Moody replaced fellow former Australia player John Dyson as Sri Lanka's coach in 2005 and since then the 1996 champions have undergone a resurgence in form that has seen them emerge as serious contenders for the title in the Caribbean.
During last year's tour of England, Moody coped with the fall-out from the Test 'retirement' and then return of star batsman Sanath Jayasuriya to help his young side draw a Test series 1-1 before they triumphed 5-0 in the subsequent one-dayers against England.
Jayawardene, speaking after Wednesday's Super Eights cliffhanger against England in which Lanka held nerves to win by 2 runs, praised the impact Moody had had in broadening even the horizons of even senior players such as Jayasuriya and off-spinner Muttiah Muralitharan.
"Obviously we've enjoyed playing under him. The thing he's done is push everyone in the team from Murali to Sanath to myself to the youngest player in the camp, he has pushed us not to stay in our comfort zones and push ourselves to see what's out there," explained Jayawardene.
"Every day we go for practices, we don't just turn up. We make sure we try and learn something new as batsmen and bowlers.
"That's something special Tom has brought into this team and obviously a lot of the guys like the way he handles players as well."
He said it was no surprise to him that 41-year-old Western Australian Moody, who played eight Tests and 76 one-day internationals, had been linked with other jobs.
"When people are successful that can happen. He wanted to take us to the World Cup and then see where he wanted to be. It's his decision."
But he added that whether Moody stayed or went, Sri Lanka cricket would remain on an upward curve.
"We have to acknowledge he's been brilliant but Sri Lanka cricket, whether he stays or not, will not divert from where we are going. We've developed teams for the last 10 years and we are heading in the right direction.
"If a new coach comes in he'll bring something new to the table and we'll just have to adapt to that. If Tom stays it will be brilliant as well and then we will try to push forward."