Having won the toss and opted to bowl on Sunday, Ireland made a solid start in the field, restricting Sri Lanka to 3-71 by the end of the 11th over after George Dockrell picked up two wickets.
Kusal Mendis finally gave the home crowd something to get behind as he pushed the total on, but then was fortunate to be dropped three times in the 17th over as Matthew Humphreys went for 21 runs.
In the penultimate over, Barry McCarthy took two wickets in two balls to dismiss Kamindu Mendis for 44 off just 19 balls and Sri Lanka captain Dasun Shanaka for a golden duck.
Kusal Mendis then brought up his half-century - finishing unbeaten on 56 off 43 deliveries, with five fours - as the co-hosts made 6-163.
Ireland lost captain Paul Stirling (six) in the fourth over of their reply when he was bowled by Maheesh Theekshana, but a determined 34 from Ross Adair saw them on to 2-72 at the halfway stage.
Lorcan Tucker (21) and Harry Tector (40) continued to try to eat away at the run-chase and Ireland were 2-104 after 14 overs, needing 60 from the last six.
But Sri Lanka fought back to make regular breakthroughs - including Theekshana dismissing Ben Calitz and Gareth Delany in successive deliveries - as Ireland finished short, all out for 143 with one ball left.
They'd losing their last eight wickets for 38, as Wanindu Hasaranga and Theekshana claimed three wickets each.
Ireland will be Australia's first opponents on Wednesday, while Sri Lanka face Oman in Pallekele on Thursday.
Stirling accepted his side had probably let the match slip away at crucial points.
"I felt they got 15 to 20 too many," he said. "At the start of the day, we would have been happy chasing it, but you could find 20 runs almost anywhere in the match.
"When the match was on the line, we were not as clinical as we wanted to be and a bit sloppy in the field, which is disappointing.
"Experience told today at the end of both innings, and it was the difference. They defended well at the back end, they upped the ante and put the squeeze on."
