The nations meet in Brasilia on Sunday before group rivals France and Honduras face off later in the day.
As Mendez seeks to help guide Ecuador to the knockout stages in their third World Cup, he feels an opening-game victory is vital to their chances.
"The first match will be important not to lose. Against Switzerland it is for is six points, not three," he told EFE.
"They are a direct rival and we have to get the points. (A win) gives us the ability to fight against France and against Honduras."
Mendez has 111 caps for his country and was part of the side that made it to the last 16 of the World Cup in 2006.
After Ecuador missed out on qualification for the competition in 2010, the 35-year-old feels he is in a better frame of mind this time around.
"At the first World Cup I did not know where to step or what to say," he added.
"Today it is a different World Cup for me, from another point of view.
"We are in the land of football, where it is played very well. Hopefully I can have a great tournament."
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