Head coach Gregor Townsend was disappointed at aspects of Glasgow's performance as the Pro12 champions fell to their third defeat in five matches.
Warriors lost two players to the sin bin in the second half in Dublin as they were defeated 23-18 by Leinster.
"Before tonight I was really pleased how we had performed," said Townsend.
"Tonight we just missed those little bits of detail. I'll have to make sure we get those bits right and our discipline has to be much better."
Reflecting on the Pro12 campaign to date, Townsend told BBC Scotland: "We had a slow start against Scarlets but showed great character to almost get a win and after that we have played pretty well.
"We almost won in Munster, got a good win against Connacht and got a bonus-point win against the Dragons.
"Against Leinster, in the second half we were down to 14 men for 20 minutes so that's probably why they had more possession and got the points on the board."
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Hooker Pat MacArthur was yellow carded on the stroke of half-time and Fijian winger Taqele Naiyaravoro was later sin-binned for slapping the ball out of play.
That infringement resulted in the Irish side being awarded a penalty try, which was subsequently converted as Leinster moved in front late in the game.
Townsend respected the referee's right to sin-bin the duo but disagreed with the award of a penalty try as Leinster's Fergus McFadden and Naiyaravoro engaged in a foot race to reach the ball in the try zone.
He said: "When I saw the replay I thought it was McFadden who had touched it.
"They both reached for the ball, neither of them managed to catch it. If it was our winger who knocked it back then it's a yellow card.
"But I can't believe it was a penalty try because McFadden missed it and the ball was bouncing behind him to Sean Lamont, who was there in cover.
"It was a big call by the referee and obviously it nudged Leinster ahead and, down to 14 men, we couldn't find a way to win the game.
"However, I thought the defensive line speed was excellent, we put pressure on Leinster's attack and I felt we made good decisions in our attack at times.
"We created a try and we got a couple of penalties for our efforts as well.
"But there were a couple of bits of detail we didn't get right. It's disappointing when you get opportunities close to the Leinster try line and someone just misses a play or doesn't make the right move. We gave possession up too easily."