But they came up against an inspired Paddy Jackson, the fly-half kicking 14 of Ulster's 19 points, as Mark Anscombe's men made it ten wins from ten.
Jackson's opposite number Aled Thomas kicked all 12 of Scarlets' points, including one in the last minute to secure a losing bonus point for his side.
With just over 15 minutes remaining, and the scoreline 19-9, Dan Tuohy was sin-binned for not rolling away, but the Scarlets couldn't take advantage.
And although pleased his troops were able to secure a losing bonus point, Easterby was still frustrated with his side's performance.
"We still had a strong side out there and we went into the game having won last weekend, we were playing at home, there are no excuses from us," said Easterby, speaking to the South Wales Evening Post.
"We did get better in the second half, but we lacked accuracy in certain areas and put pressure on ourselves.
"The scoreboard reflected that we were beaten to most things on the day.
"That losing bonus point might be a factor in five months time, but right now I am more concerned with us not winning the game."
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