Gareth Davies scored two tries while Rhys Priestland converted both and added a penalty but for the Blues, Alex Cuthbert, Andries Pretorius and Harry Robinson all crossed to leave the score 17-17 with 16 minutes to go.
Dan Parks put the Blues ahead with a penalty but Scarlets wing Liam Williams hit back with a try before a penalty try eventually handed the hosts the victory.
Jenkins, who is heading to Toulon, is among 11 players departing the Blues over the summer with Phil Davies coming in as director of rugby.
But despite the drastic overhaul, Jenkins is convinced the future is bright for Cardiff.
"It's going to be something different, I'm looking to getting out to France and getting on with it," said Jenkins.
"There's a big tour to come with Wales first but then it's all go and I'm looking forward to it.
"We had nothing to lose against the Scarlets and I thought a lot of the younger players were excellent and we played some good stuff and I think that bodes well for the future.
"I think this club is in good hands. I was given a [commemorative] shirt last week and that is obviously going to take pride of place in my house."
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