Gyasi and Spezia have impressed in their debut Serie A season, despite the lingering goal of survival hanging around them.
Spezia is just three points adrift of the relegation zone, with four games remaining.
"We kept the core of last year's team and that helped us integrating the players who have arrived in the summer," Gyasi told BBC Sports.
"Before I actually judge our performance, I'd rather wait and put the cherry on the cake. We did well so far but we have to top it with the right finish!
"We are a great group and we have a common goal," Gyasi added.
"The club takes care of everything and we just need to concentrate on our job on the pitch."
Spezia has recorded some gigantic feats in their first campaign, beating AC Milan and Napoli, as well as picking points against Atalanta and champions, elect Inter Milan.
The 27-year-old Ghanaian has been a key cog in the side and attributes his performances to the influence of manager Vicenza Italiano.
"A player has to be lucky and meet the perfect manager and that has happened to me, I feel his confidence and that made me develop greatly." Gyasi insisted.
"It's my third year here, Spezia feels like a second home to me. I have found the necessary stability and most of this is down to the manager." Read Full Story
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