Universidad are fighting for their first international title and face Liga Deportiva Universitaria on Wednesday night. The Ecuadorian side won the tournament in 2009, but will have to overcome a 1-0 deficit from the first leg at home last week.
Diaz told reporters in Santiago: "This is the most important game in the history of the club. We are calm and not excessively confident, but we are aware of the importance this match has."
He added: "Our goal is winning the match. We must be ready for that. We hope this trophy we've been dreaming of for such a long time stays here with us."
Universidad coach Jorge Sampaoli is not expecting an easy game against Liga. "They will be very hard to us. I hope we can attack a lot," he said. "They have very experienced players who can hurt us any time.
"We have only taken a little advantage in a 180-minute match against a team who have already won four finals."
Liga not giving up
Liga attacking midfielder Luis Bolanos, who has recovered from a leg injury, told the club's website that they still have a chance in Santiago.
He said: "We need a one-goal difference. Away goals are not considered in the finals. We are going to Chile dreaming of a positive result and we are committed to that.
"We have to take care in defence. They have very fast players and can hurt us, but we can complicate any rivals we play. This team has enough experience to face these type of difficulties. We'll fight until the end. No question about it."
Liga manager Edgardo Bauza, who took the team to the 2008 Copa Libertadores title, said: "The most important thing is to hold our heads high when the match is over because that would mean we did our job well. We'll do our best as in any match we play. Two very good rivals are meeting."