Barzagli said that Juve expect to continue that streak and believes that morale in Turin is at an all-time high.
He told reporters: "We put in a great performance and are very happy, especially as we were worried, knowing Roma's qualities.
"In the second half we could've controlled the game a little better, but in any case at the end of the day we did well.
"We have reinforced the squad and have even more belief than last season, but we know Serie A is always going to be difficult and on top of that we've got Champions League commitments."
Juve are top of Serie A after collecting 16 points from their opening six league games.