The Bianconeri successfully nullified the resurgent Tuscan side, with some particularly staunch defending in the second half.
Barzagli insisted that his side knew the game would be difficult and stressed the importance of staying "out in front" in the title race.
"It's always important to be able to stay out in front," the 31-year-old told reporters after the game.
"We knew that today's game would be difficult. We did well to find the breakthrough and had to tough it out a bit in the second half but that's fine.
"Tomorrow we'll keep an eye on Napoli's game, as we do with all the others. We'll prepare in the best possible way for Friday's encounter."
Next up for Juventus is a title-decider against Napoli next Sunday.