The Spain striker scored the only goal as Marcelino's side claimed a 1-0 second-leg win in their semi-final with Real Betis on Thursday, thereby securing a 3-2 aggregate triumph.
It means Valencia will play in the final for the first time since they last won the trophy in 2008 under Ronald Koeman, with the match taking place just two months after their 100th birthday.
And Rodrigo says facing Barca will be a moment to savour for everyone associated with the club.
"It's a very special season with the centenary and we're very happy to reach the final," he said, as quoted by Mundo Deportivo.
"We've played a very complete knockout tie. We deserve to be in the final.
"We knew they [would] have a lot of possession but that we were going to have a chance on the break.
"This is a final for everyone, for the club, the squad and the fans."
Betis, who led 2-0 in the first leg before conceding twice in the second half, dominated possession at Mestalla but could not find a breakthrough.
It means Betis miss the opportunity to play in the final at their own Benito Villamarin Stadium in Seville on May 25.
"We really wanted to be in the final," said the former Barca man. "We wanted to get there, and we were able to, but that's football, and not everyone can win.
"It's a big blow. We have to be self-critical but with our heads held high and all pulling in the same direction.
"I'm very proud of the team and the fans. We apologise to them, and we congratulate Valencia."