The Lupi were left despondent after a solitary Senad Lulic goal gave their cross-city rivals a 1-0 win in May's tournament decider.
However, Garcia feels that defeating Lazio 2-0 in their fourth game of their current Serie A campaign allowed them to exorcise their demons and pave the way for a surprise bid for this season's Scudetto.
"There have been several decisive episodes during this season," the 49-year-old Frenchman told a press conference.
"That started with [Daniele] De Rossi's goal on the first day against Livorno [the first in a 2-0 win]. The cup final turned the club upside down. There were objections from some of our fans, some thought that the match against Lazio this season came too soon.
"Instead, I think it was the right time to put a lid on the past."
The former Lille boss also hailed Giallorossi captain Francesco Totti, who he says has played a key role in Roma's resurgence this term.
"He's an icon and an outstanding leader as well as a fantastic player," Garcia said of the Italian forward.
"At 37, he no longer has all the capability as he had before but he is a big player in the history of football.
"From experience, I decided to be honest with him, which was what he expected. Winning something with him that would be great."
Roma face Sampdoria on Sunday and sit second in Serie A with 51 points from 22 games, nine behind Juventus, who have played a game more.