The Italian new boys appeared on course for the first victory of their brief history after Matteo Pratichetti touched down on the hour.
But a fortuitous bounce of the ball helped Kristian Phillips mark his first start for the Scarlets with a crucial match-winning try.
“At the end of the day it was a win and four points that we desperately wanted but there was little else to take from that performance,” said Easterby.
“If I was to judge the effort of the players, it would be eight or nine out of ten. But as for execution and accuracy, that was more like two.
“We put a lot of pressure on ourselves with our mistakes. We played in the wrong areas and in greasy conditions, we turned the ball over which allowed them to get out of dangerous positions.
“As a team there is a lot to learn from this but at least we still got the win.”
The Scarlets trailed 3-6 at the interval but Aled Thomas booted the hosts into the lead with a pair of penalties while Tito Tebaldi was in the sin-bin.
But the lead quickly returned to the Italians, who capitalised on a succession of errors from Easterby’s side.
After spilling possession, Zebre kicked down field and the Scarlets twice failed to deal with the loose ball to allow Ferrarini to brake clear. He then combined with Tibaldi, who sent Pratichetti over in the corner.
Halangahu slotted the conversion to hand his side an unlikely 13-9 lead. But the Scarlets fought their way back and Thomas chipped away before Phillips raced clear to let his side off the hook.
