Warnapura starred with scores of 120 and 62 in Sri Lanka's opening Test win by 121 runs against West Indies last week at Providence, and Thushara offered steady support to the elite bowling duo of Chaminda Vaas and Muttiah Muralitharan with match figures of five wickets for 129 runs from 37.5overs.
"These two guys have played good first-class cricket back home and play a little bit of league cricket in England so know their way around the park," Jayawardene said.
"We can always call them up and say this is your opportunity.
"They have waited a long time for this opportunity, and now they will get an extended run - whether they make runs or not, or whether they take wickets or not.
"So we have not put them under any pressure on this tour, and told them that if they fail that they will lose their place.
They will get an extended run, and this is probably why they have responded to the challenge in this way."
The retirements of former captains Sanath Jayasuriya and Marvan Atapa