The Giallorossi edged the Serie A leaders 1-0 in Rome on Tuesday evening to progress to the semi-finals of the Coppa Italia.
Roma had lost 3-0 at Juventus earlier this month and are eight points behind them in the standings.
"This was a win that we wanted to get at all costs," Roma captain Francesco Totti said.
"We want to bounce back from our defeat in Turin and we proved to be at the same standard as Juve.
"In my opinion, there is not much difference between us and them even though they have a good lead in Serie A.
"We are having a fantastic season but they are doing better than us."
Roma midfielder Daniele De Rossi was also delighted to have reached the last four of the Coppa Italia for a second straight year.
The Giallorossi were runners-up in the competition last season behind city rivals Lazio.
"It was important for us to win this game for many reasons," De Rossi said. "First to reach the semi-finals of an important competition.
"We wanted to send a message as Juve are dominating Italian football in recent years.
"There were 60,000 fans at the Stadio Olimpico to watch this quarter-final and to have given them joy makes us very happy."
Roma will now play the winners of next week's quarter-final tie between Napoli and Lazio.
"We hope it will be Napoli," De Rossi said. "Napoli is proving to be much stronger this season."
Juventus coach Antonio Conte felt his side did not deserve to lose last night.
Gervinho's goal with 11 minutes remaining stunned Juve who had earlier been denied the lead.
Federico Peluso's header from Mauricio Isla's cross had found the net but the goal was disallowed as the ball had previously gone out of play.
"I didn't see the Roma players protesting when the ball went in," Conte said. "But perhaps the ball was out.
"In any case, mistakes can happen.
"We are obviously disappointed to be out of the competition but my players did their best.
"It wasn't easy to play against this Roma."