Juve needed a 77th-minute equalizer from Dejan Kulusevski to earn a 1-1 draw at home to Hellas Verona, who went ahead through Andrea Favilli on Sunday.
The Serie A champions are winless in two consecutive league games against Verona for the first time since 1989 as Juve moved onto nine points through five games.
Juve host Barca in the Champions League on Wednesday, but Pirlo was unfazed, saying he expected a different type of game.
"No, I am not worried ahead of Barcelona, because they're two completely different games, with two different styles of play," the Juve head coach told a news conference.
"As I said earlier, Atalanta like Verona play in a completely different way compared to Barcelona, therefore when you play against this kind of team it's a kind of game of its own.
"You have to try and do certain things, which we tried to do during the game."
The result left Juve three points behind leaders Milan, who host Roma on Monday.
But Pirlo, who only took charge in August, is remaining upbeat about the direction his side are heading in.
"No, I am not worried [about the draws] because we are under construction," he said.
"Of course, we're sorry we're dropping points along the way, but we're on the right path and we are building a long-term project.
"It's only the fifth game we play together and for our future I can only see positive things."