Jack Conan and a penalty try did most of the damage for the hosts while a man-of-the-match display from Josh van der Flier ensured the Welshmen left Dublin without so much as a losing bonus point.
The GUINNESS PRO12 now takes a break for three weeks but Leinster's next match sees them host Newport Gwent Dragons, who they lost to both home and away last term, on October 3.
And Cullen is convinced that while there were plenty of positives against the Blues, there is more to come against the Dragons.
"We felt we didn't fire out much of a shot last week against Edinburgh and our ball retention was really, really poor," he explained.
"Sometimes you get that with inexperienced guys and the occasion was a big step up for some of them.
"So it was pleasing that we played some phases against the Blues even though we couldn't quite nail everything we would have liked.
"But that's the challenge as coaches - there is plenty to work on. We'll take a week away from it now and then focus on the Dragons for three weeks time.
"I think it's good for the guys' confidence but it will be a different challenge against the Dragons in a few weeks time.
"They caused us a lot of problems last year beating us home and away. So it's important that we take the win, take the four points and knuckle down now."
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