The Llanelli-based region reached the play-off semi-finals last season, where they were comfortably beaten by Ulster.
But Easterby has been encouraged by the Scarlets’ pre-season preparations, despite losing to Exeter Chiefs and drawing with London Welsh.
They face Gloucester on Friday before kicking off their league campaign against reigning champions Leinster and Easterby is quietly optimistic.
“We have to have higher expectations of ourselves and look to our goals and work hard to achieve more this season,” said Easterby.
“Our challenge is to improve on what we did last year, if we do that we have a good chance of making top four again this season and going one step further.”
Wales fly-half Rhys Priestland is set to make his latest comeback from an Achilles problem, while fellow international trio Ken Owens, Liam Williams and skipper Rob McCusker will make their first appearances of the summer in the Kingsholm clash
“We’ll pick as strong a side as we can, which will hopefully set us up nicely for the Leinster game,” said Easterby.
“I think we’re in a far better position going into the new season than we were at the same stage last season and I’m happy with the progress that we’ve made throughout the pre-season.
“Hopefully, we can produce a good performance against Gloucester on Friday night.
“Wales’s loss is our gain in the sense that a number of guys including Rhys, Scott (Williams), Josh (Turnbull) and Ken didn’t tour.
“They have had a good pre-season, which they don’t get that often any more. It’s been an opportunity for them to get niggles seen to and build themselves ready for the new season.
“I’ve also felt far more comfortable that we have had our players in earlier. It was difficult for us last year because the South Africans came in late with little or no time to bed in.
“What we’ve had now is some continuity and less disruption. We’ve had a chance to build some continuity and strong team work.”
