After the break Williams added another penalty before converting Johan Synman's 47th-minute try for a 21-5 lead.
Williams struck another penalty soon after but Giovanbattista Venditti hit back with Zebre's second try of the match on 57 minutes and that was the end of the scoring - the Scarlets running out 24-10 winners.
And Easterby, whose side are currently fifth but would be fourth, above the Ospreys had they scored four tries, is keeping his fingers crossed it doesn't come back to haunt them.
"It certainly had an impact on fatigue, and the playing surface didn't help either," he told Wales Online.
"They won 62 per cent of the possession, and we were forced to make a lot of tackles, which also took a lot out of us.
"We played some good stuff in the five or ten minutes either side of half-time but we couldn't grab hold of the game after that and we were holding on in the end.
"Hopefully we won't be left to regret it come the end of the season.
"The boys were asked to dig in, but credit to them, that is exactly what they did.
"Getting the four points here was our primary goal, and now that we've done that, we can go home, patch up a few of the boys and get everyone back on their feet for the double header next week."
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