After a good start to the season the Scarlets are very much in the battle for a RaboDirect PRO12 semi-final spot, knowing that it is in their own hands.
And Easterby insists his team will need to be at their best on Friday night to ensure they don't become the Italian franchise's first-ever victims.
He said: "It's been a very positive week back in full training at Parc y Scarlets, with the boost of the international players coming back energised by their victory in the Six Nations and we are now clearly focused as a group on these next five games which we have to win to retain our control on a top four finish.
"Zebre may have lost a lot of games this year but have come very close to teams at nearly every point - so we have to be really focused on our job in hand as players and as coaches. They will be very competitive and we will not be going out there underestimating what we need to do to get a result.
"The Italian players will be very upbeat after Italy's finish to the Six Nations and with that they will post a real threat to us and our ability to retain our control on our play-off ambitions.
"A play-off place is still in our control and that's up to us to follow through with that now with results."
Easterby has added three of Wales Six Nations winners into his starting lineup, with Liam Williams, Aaron Shingler and Matthew Rees all starting, while Scott Williams comes on to the bench.
Zebre have also welcomed back two of Italy's Six Nations starters into their starting lineup, with Giovanbattista Venditti in the unfamiliar position of centre and Quintin Geldenhuys in the second row.
Luciano Orquera will be on the bench as the Zebre try to record a first win of the season, having fallen just short last time out away to Connacht.
Skipper Marco Bortolami was forced to pull out with injury but is confident his side are ready to break their duck.
He said: "At this level there is no improvising and you can't reinvent anything. It's a long road but we know we are in a good place.
"The handicap we began with was an important one but we are where we are, we need to take the step from losing by a point to winning.
"The return of the internationals could help us make that step, even if we will have to play teams fighting for play-offs. We will not let anything lie, but we have faith. The win is not far away."
At Stadio XXV Aprile , 7pm local time (6pm UK & Ireland) Live on Sportitalia
Referee: Peter Fitzgibbon (IRFU, 45th competition game)
Assistant Referees: Stefano Penne, Stefano Roscini (both FIR)
Citing Commissioner: Alberto Recaldini (FIR)
TMO: Carlo Damasco (FIR)