The Scarlets put up a brave performance on Friday night but couldn't overcome a strong Bourgoin side in France, losing 54-38 in the Heineken Cup.
"I thought we played well against Bourgoin and were more than unlucky to lose the game," said Jenkins. "The difference between the two sides on the night was that we made too many errors.
"Three of those errors cost us points and we must cut them out if we are to win against Ulster. We dominated the match but it's no good having most of the play if you don't convert it into points."
While Llanelli's Heineken Cup aspirations are still alive, a defeat on Friday night will spell the end of their Celtic League campaign.
"It will be a huge disappointment not to reach the knockout stages of the competition," said Jenkins.
"I think we've made enough progress this season to proceed further but we'll have to earn our victory.
"Ulster present us with a very different challenge to Bourgoin - the only similarity is that they are both very good sides and will both be tough matches.
"But, we're more than capable of going there and getting a win. We're a decent team and if we play to our full ability then we can get the result we want."
Llanelli will spend most of this week working on eradicating the mistakes they made against Bourgoin.
"We'll work the players hard in training and the management team will do the homework," said Jenkins.
"The players were very disappointed after the Bourgoin game and this match against Ulster gives them a perfect opportunity to redeem themselves."
Llanelli announce their side to face Ulster on Wednesday.