Brazilian Dani Alves' fortuitous strike moments after the interval, a long-range effort helped into the net by Rosanero defender Edoardo Goldaniga, proved to be the difference in a physical and hard-fought encounter on Saturday evening in Sicily.
After dominating proceedings in the first period, Massimiliano Allegri's men were forced to defend resolutely towards the end as the home side pushed hard for an equaliser that ultimately was not forthcoming.
"We must improve from every point of view. We made a lot of technical errors and we have to make sure we're in the contest for every second of the game, otherwise we risk making life difficult for ourselves," Bonucci told Juventus' website.
The Italian defender was frank in his assessment of the team's performance at the Stadio Renzo Barbera. "Palermo defended and played well, but it wasn't the real Juventus tonight. All these errors in technique aren't like us," he admitted.
Nevertheless, Bonucci feels there were some positives to draw from the encounter that helped them continue to sit at the top of the Serie A, with a lead of one point against last season's runners-up Napoli.
"We've picked up six points in two games without conceding and we put in the hard yards after scoring tonight. Now we're focusing on Dinamo Zagreb: let's win there and pick up our first win of the group stage."
Juventus head coach Massimilano Allegri was also happy to have picked up all the three points.
"We wanted to win and not concede any goals," the Bianconeri tactician revealed after the game. "We got the points and showed the right spirit, but we need to make fewer mistakes technically.
"Nevertheless, we'll take the three points and now we start preparations for the next two games before the international break. I liked the fact that when we went down to ten men we were able to hold on for the victory."
Allegri opted for an essentially new strike force at the Stadio Renzo Barbera, as Gonzalo Higuain and Mario Mandzukic had only played together in friendlies before Saturday.
"Their job was to give options to the midfielders and I think they played well. They didn't link up much between themselves but that's normal given their attributes, plus they worked hard at the end," he said.
