Scarlets full-back Dan Newton converted while Aled Thomas' second-half penalty was to prove decisive as the Dragons on recorded two Jason Tovey kicks.
They missed five crucial penalties one from Tovey and four from Lewis Robling and head coach Darren Edwards was in doubt as to what cost them victory against the understrength Scarlets.
"Goal-kicking? I suppose you can't hide away from that fact. Scarlets gave away 19 penalties and we missed four from in front of the posts," said the Dragons head coach.
"We should have been able to put Scarlets away because, on paper, we were the stronger team.We're competitive but we needed the win as that would have given us the confidence to turn the corner."
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