Sri Lanka benefitted four times under the rule during the opening Test against India here before winning by a record innings and 239 runs on Saturday to gain a 1-0 lead in the three-match series.
The rule, on trial in the ongoing series, allows a batsman or fielding captain to request a review of any decision by referring it to the third official monitoring television replays.
"I am all for it, not because most of the referrals went our way but because we managed to rectify obvious mistakes," Jayawardene said after the match.
Sri Lankan batsman Tillakaratne Dilshan was the first beneficiary. He was on one when initially given out caught by umpire Mark Benson of England on Thursday, but asked the official to review the decision.
Benson consulted TV umpire Rudi Koertzen of South Africa before changing his decision. Dilshan went on to score 125 not out.
Indian batsmen Virender Sehwag, Sachin Tendulkar and Rahul Dravid were initially given not out by on-field officials, who changed their decisions after consulting the TV umpire.
"We need not think negatively about it. If it was not there, we probably would have had four bad decisions go against us in this match," said the Sri Lankan skipper.
"The decisions of both Tendulkar and Dravid were tough for the umpires, especially when you have (Muttiah) Muralitharan and (Ajantha) Mendis going at the batsmen on these kinds of tracks."
Off-spin maverick Muralitharan was named man of the match for grabbing 11 wickets, while debutant spinner Mendis took eight wickets.
"It is very good. No team can complain that they lost because of bad decisions," said Muralitharan, the world's leading wicket-taker with 746 scalps in 121 Tests.
Defeated India captain Anil Kumble said it was too early to comment on the rule.
"A couple of calls were negated, but I think it is something that we will have to take forward. It is a bit too early to comment," he said.
A top International Cricket Council (ICC) official recently said here he did not believe the rule would undermine the on-field umpires' authority as their word was still "final".
"It is an extension of the appeal. It doesn't undermine their roles. Their skill as umpires is still paramount. They have to make the decision (after consulting the TV umpire)," said ICC general manager Dave Richardson.
"I am confident it will work quite well. We must not forget what the real objective of this process is -- and that is to avoid obvious and clear mistakes."
Each team is allowed three unsuccessful review requests per innings but if one is successful they will get an additional appeal.
The rule applies for all dismissals except "timed out" when an incoming batsman is out if he takes too long to arrive at the crease after the fall of the previous wicket.
The second Test starts in Galle on Thursday.