Stuart Hogg gave Glasgow a good start on his first appearance of the season, scoring the game's opening try. Leinster hit back strongly, though, with two tries from prop Cian Healy and one from Jonathan Sexton giving the visitors a firm grip on the match.
Tommy Seymour's try briefly hinted at a Warriors revival, but they never truly looked like hauling in their opponents, and Noel Reid's touchdown sealed the bonus-point win for the three-time champions.
Head coach Dave Rennie says the Warriors may now prioritise the PRO14 above the Champions Cup.
Speaking to BBC Scotland, Rennie said: "Maybe PRO14 is going to be more of a focus. We'll probably have a look at it in December. Certainly with all our international boys going to be in and out, and depending on our injury ward, it may determine the mind-set we take into Montpellier in December.
"We got outmuscled today, we lost the collisions. They carried strongly and got in behind us. When we carried they defended well in front of us.
"They're a good side. I think we're better than what we put on the park today but it's a lesson.
"We lost the penalty count 10-5, which allowed them to put us in the corner. We're aware teams are going to attempt to do that.
"We got ourselves back in the game. I thought Tommy's try was a great example of building pressure, a high skill-set mixed in with some brutality. But too many errors today and they choked us down our end of the field."