Conte unhappy with referee
Roma won the match 1-0 thanks to a goal from Gervinho in the 79th minute, but there were two controversial incidents that had a massive impact on the result.
Federico Peluso had the ball in the back of the net in the opening minute of the second half, but the linesman ruled it out as Mauricio Isla's cross appeared to go out of play.
"In all honesty from the footage it looks like it's in play by a metre, at least. Look at the ball and where the crossbar is, it seems to be in play," Conte said.
"I repeat, referees can make mistakes, but it looks like it's in and quite a bit in, at that.
"Looking at the reaction of the Roma players, who didn't protest, they even look like they are blessed by the linesman lifting his flag.
"Maybe it's better that it happened against us, otherwise imagine the chaos that would've emerged with people talking about 'help'."
Conte was also aggrieved about the decision to only give Roma defender Mehdi Benatia a yellow for what Juve thought was a last-man foul on Sebastian Giovinco.
"I thought that could be considered a last-man foul. I asked the fourth official that too," he said.
"In any case, I don't wish to comment on the referee, he made this decision and that's all."
Juventus last won the Coppa Italia in 1995 and Conte was left disappointed his side were knocked out of this year's tournament.
"It's a shame that we were eliminated from a tournament. I have nothing more to ask from the lads, as in the past we always used the Coppa Italia to rotate the squad also to help the team grow in future," he said.
"I had some positive responses and the regret remains that we conceded a goal during our best period of the game."