Beating 2012 English Champions Harlequins at The Twickenham Stoop was the result of the round when European competition got underway three-and-a-half weeks ago, while sharing the spoils with French giants Racing Metro back in Wales was no mean feat either.
But what followed didn't match the same standards as only a last-gasp penalty from Wales fly-half Rhys Priestland saved the Scarlets' blushes at the Stadio XXV Aprile.
Easterby admits that it was a definite setback given what had gone before and he has told his players that improvements must be made against Ulster on Saturday night.
"The Ulster game gives opportunities to players who have been on the fringe this season and it's a chance to put right what the players in Zebre didn't," said Easterby, who will be without the likes of Jonathan Davies and Scott Williams this week as Wales get set for their Dove Men Series opener with South Africa on November 9.
"We are obviously losing a group of players this week and we knew that was going to be the case and we have to deal with that.
"No disrespect to Zebre, but with the team we had out and on the back of our two good performances in Europe, we should be getting results at places like that.
"For us it felt like a loss after the game, but we were our own worst enemies. Maybe we expected things to happen, instead of trying to make things happen."
Injured co-captain Rob McCusker agrees with Easterby that the Round 6 encounter was a far from inspiring one but he insists he and his team-mates won't be dwelling on the disappointment.
McCusker, who is still out of action with a calf problem, knows they should have given a better account of themselves in Italy but he believes the squad will bounce back, especially as they have the extra motivation of gaining revenge for their semi-final defeat at Ravenhill last season.
"It's not all doom and gloom and certainly no cause to hit alarm bells. There are games like this in a season where a poor result just spurs you on more," McCusker wrote in his column in the South Wales Evening Post.
"Our two opening Heineken Cup games showed that the current group of Scarlets are quite capable of producing outstanding performances.
"Yes, Zebre was a game we should have won but we'll take the draw for now and shift our focus to Ulster. Ulster are a team we owe a performance to after the semi-final of the PRO12 last season.
"We didn't give the best account of ourselves at Ravenhill that evening and have felt aggrieved ever since. Now we have a great chance of laying some of those demons to rest against a side who have become somewhat of a bogey team for us over the last couple of years.
"Beating a quality side like Ulster will certainly do our league challenge the world of good and leave us in a decent state for when we take a break from the Rabo and kick off our LV= Cup campaign."