The 37-year-old has made 15 appearances for the Bianconeri this season but hasn't found the net prior to the match against Roma on Tuesday night.
Del Piero admitted that while he wasn't specifically bothered by the recent goal drought, he is relieved to continue his record of scoring in 19 straight campaigns for Juventus.
He said on the club's official website: "Not finding the target until today didn't make me anxious, but I've shaken off a slight burden, because both myself and many fans had been waiting for this goal.
"It was also nice to score because the goal wasn't just a moment, it came during a good performance, made up of plenty of movement and exchanges with team-mates.
"I wanted to play well, get through to the next round, and then score a goal. We're all working towards the same objective with great commitment."
The 37-year-old's contract with Juventus is set to expire at the end of this season and he is set to leave the Turin giants.