Argentina have not lifted the trophy since Basile guided them to the second of two titles won under his stewardship in 1993.
Following that success Argentina have twice lost in the final, with Basile denied a third Copa triumph in his second stint in charge courtesy of a 3-0 defeat to Brazil in 2007.
The World Cup runners-up lost in the quarter-finals on home soil in 2011 but, following their efforts in Brazil last year, Argentina will be expected by many to reach the Copa final in Santiago.
However, Basile told Perform: "The opponents are well-matched. One day you can wake up and lose and that's it, goodbye, you're out.
"We always have top-level players, more so those that play in Europe, and especially forward players… we have big stars and goal-scorers all over the world, that is unquestionable.
"But look at Brazil for example. They are five-time champions [at the World Cup] and, on home soil, it was the worst team in Brazil's history, it was hard to believe. The thing is that other teams are getting stronger.
"The Copa America is very difficult, the teams from the continent have become much stronger. Now all the teams, including at World Cups, do well and are of the top level.
"For that reason it's difficult. Now you don't just win matches because of your name. Good teams win matches now and they are all very even.
"No Argentina team of mine ever lost a game at the Copa America until the final of 2007. Now I want us to win it again, because Chile [the scene of Argentina's 1991 glory] is the ideal venue for Argentina, a lucky venue."
