Fly-half Finn Russell kicked all Glasgow's points as the Scottish side stayed within touching distance of the defending champions in the first half, trailing just 14-12 at the break.
But with the wind behind them in the second half Leinster's experience told as they scored 20 unanswered points to become the first side to retain the title.
Kellock admitted that his side had made too many errors and challenged them to go one better next season.
"We spoke in the changing room about how we need to use this again the way we've used these semi-final losses (in the past two seasons) and push forward," Kellock said.
"It hurts to lose a semi-final, and it hurts more to lose a final. There were a few key points in the game where we needed to get a break and I believe we pushed them really hard. Although the scoreline was comfortable, if we got the right break at the right time, we could have gone on and won that.
"But on the day the better team won. It's hard to take because we went out with the intention of playing the way we have been playing.
"We will look at what we have to do to get better. The emotion I am trying to force to the front is the pride at the effort that has gone in. What a two weeks it's been, to win against Munster, the build-up, the fans when we entered into the ground were incredible.
"Because we've lost it, we can't let the good work that has gone in - not only on the park, but the good work in building this club - slip. We've got to keep pushing forward, and if we lose a final to win one next year, then you would take that."
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