But Cullen was not satisfied.
"We get over their try line, we have a couple of five metre scrums - we need to be better at capitalising on these really good situations we get ourselves in," he said.
"With some changes we probably lose our way a little bit, then as the game wears on we get a little bit disjointed.
"Ulster defended really well as well, so you've got to give them credit. From our own end we just need to look at ourselves and how we can capitalise when we get in those good positions with really good opportunities."
Victory comes hot in the heels of last weekend's European defeat to Bath.
And Cullen was delighted to see his men bounce back so quickly.
"There was a lot of really good effort. The lads have had a tough couple of weeks. Again, it was a short turnaround the six days leading into the game," said Cullen, whose team travel to Glasgow Warriors next Saturday.
"The flipside of that is we've an eight-day turnaround now so guys get a bit of recovery time over the weekend and we can actually do a proper week's training, whereas the last couple of weeks, those six days, it limits what you can actually do, with a few injuries on top of that as well."
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