"I wouldn't have got the bails off in the first place,'' he said.
"I would try and keep it nice and clean.''
Thirimanne - then 44 not out - looked unimpressed as umpires Paul Reiffel and Billy Bowden conferred with Indian captain Virender Sehwag after Ashwin appealed.
Sachin Tendulkar got involved and suddenly India's appeal was withdrawn.
"I think Ashwin warned him once in the previous over and next over he took the bail off and appealed,'' Sehwag said.
"The umpires discussed it with me and I said we can give him one more warning.
"If he does it again he was out.
"The International Cricket Council made the rule - if someone is taking a start then the bowler has a full right to make him run out.
"If we appeal and the umpire gave him out maybe someone will say that is not in the spirit of the game.''
Late hitting by Irfan Pathan (47) gave India some hope but it was not enough to stop them dropping to the bottom of the tri-series table with two games left.
Sri Lanka (11 points) overtook India (10) to trail leaders Australia (14) with three games in hand, starting with Friday's clash with the home side in Hobart.
Thirimanne helped Sri Lanka post 6-289 - a total that looked well beyond India when they were reduced to 1-0 after the second ball of their innings.
Sehwag - returning from injury to fill in for the suspended captain MS Dhoni - swiped at a wide ball and was caught by Nuwan Kulasekara for a duck.
Man of the match Kulasekara (3-40) then inflicted more damage.
Tendulkar - still looking for that elusive 100th international ton - flew to 22 before dragging Kulasekara on trying to shoulder arms.
And India were 3-54 in the 12th over when Kulasekara had Gautam Gambhir (29) caught behind.
Kohli looked destined to be India's saviour after he was dropped on 14 and 32 - both times by a hapless Dinesh Chandimal.
But his luck ran out when caught by Kulasekara off Thisara Perera (4-37) and India never really recovered.
Earlier, Jayawardene (45) and Tillakaratne Dilshan (51) ensured a flying start as Sri Lanka cruised to 0-95 by the 19th over after winning the toss.
- AAP