But they rallied either side of the break with first-half tries from Gareth Davies and Kristian Dacey and a penalty from the former taking them to within two points of their opponents.
Leinster replied with two tries of their own, and while Dan Fish marked his new contract with the Welsh region, it was not enough to claw back the win, eventually losing out 34-22.
It means the Blues have won just one of their last eight RaboDirect PRO12 clashes leaving them ninth in the table and the lowest of the Welsh clubs.
But despite results not going their way, Davies revealed the squad are determined to change things around.
"You can't fault the efforts of the players. There was just some fundamental errors which Leinster, a side of their quality, just capitalised on," said Davies.
"We asked the boys to front up today and show a lot of desire, I thought they did that but ultimately they just weren't good enough.
"We are where we are at the moment, all we can do is keep working week in week out as we are and the boys showing that type of commitment.
"It's frustrating that's for sure but we'll keep going and that's all we can do."
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