Juve currently sit four points clear of Inter Milan in the Italian league table, but the powerful midfielder is refusing to rest on his laurels.
"It was a good result [against Pescara], but it hasn't changed anything as far as the dressing room atmosphere is concerned," Asamoah told reporters at a fan evening in Rivara.
"We've begun well and taken many points from our start to the season, but there are still plenty of games to play. We need to hang in there, fighting all the way to the end."
Juventus face Lazio at the weekend.