The 27-year-old, who scored with an acrobatic finish 11 minutes from time, is enjoying a new lease of life after struggling at Arsenal, where his sometimes comical finishing and bizarre performances made him the object of derision.
"I am truly happy, because I scored and because we played well," said Gervinho, who will travel to Brazil to play in this summer's World Cup.
"It was very exciting for me and it wasn't easy to play against Juve, as they were well-covered defensively. We've got our revenge for the league game."
Tuesday's goal was Gervinho's fifth of the season and easily his most important since being brought to Rome by manager Rudi Garcia.
His finishing is still spotty, as evidenced by the chances he missed during Saturday's 3-0 win over Livorno, but his close control and lightning pace terrifies defenders.
After a crushing 3-0 Serie A defeat to Juve earlier this month, Roma have won four straight in the league and cup without conceding a goal.
The fans are back on their side after beginning the season with furious protests outside their Trigoria training ground and manager Garcia now seems to have won them over.
Rome will be faced with three derbies in the space of a week if Lazio beat Napoli in the cup quarters, with a league encounter scheduled for Feb. 9 sandwiched between the two midweek legs of the semi-final.
This would cause serious headaches for police and local authorities due to the threat of violence but for Roma fans it would be the perfect chance to avenge the Italian Cup final defeat that ended last year's disastrous campaign.
"It's not my problem who we face," said Gervinho.
"I am focused only on reaching the final and winning the next game."