In the first Test, they had been blown away for 143 and 168, failing to last 55 overs in either innings.
"We're not too down in the change-room about this result," Balbirnie said. "We wanted to bounce back from the disappointment of the first game, and I think we did that. If we were being hyper-critical, we could have had more runs in the first innings, because that was the best time to bat. But to have two first-time centurions - these are big moments for these cricketers. We are disappointed we didn't get a draw but we played good cricket."
This was Ireland's sixth Test. They had lost all five previous matches.
"We are very young in our Test career, so you have to take these little wins. It's the first time we've played five full days. I know there was a bit of rain around, but we got into the middle session on the fifth day, still believing we could get a draw.
"We knew it would be very tough to win the game. To take 20 wickets out there would have been very difficult. We have to take small steps. A lot of the best teams in the world haven't won Tests this early. It's going to take time. We have to make sure the players are exposed to the red ball as much as possible."
While Ireland did bat better in this game, their bowling was ineffective. They conceded 704 for 3 in Sri Lanka's only innings. Two Sri Lanka batters made double-hundreds and none were dismissed before they reached triple figures.
"We're brought up in Ireland where the wickets favour seam bowling," Balbirnie said. "It's so different here, as hot as it is, and the Kookaburra ball doesn't do a lot, particularly when it goes soft. You have high-class batters who are amazing in these conditions.
"The guys tried their hardest out there. Can't fault them at all. I know they were 700 for 3, but whenever I gave someone the ball, they had no hesitation. They just kept running in. "
"Harry played really well. He played the situation brilliantly. To see out that barrage the way he did this morning is a credit to him. He'll take a lot from this trip as a Test-match cricketer.
"A lot of our batters have done really well over here. It has been tough for the bowlers. It has not been too conducive for our seamers. But this is all a learning curve for a lot of our group. Our next Test is at Lord's, which is slightly different. Since we've come to South Asia we're three Test matches more experienced."