The South Americans, who play France on Wednesday, must match Switzerland's result against Honduras if they want a spot in the second round.
While their progress is far from secure, Mendez believes that Ecuador are capable of getting the result that they need to go through to the knockout stage.
"[France] have played very well in their two matches so far," he told FIFA.com. "Collectively they are doing well and they are getting into the box a lot, so it is going to be a totally different game for us, but to know that we have a chance of going through to the last 16 means that we will take to the field feeling confident and strong."
Mendez will make make his 111th appearance for Ecuador if he is selected to play against the French tomorrow evening.