The 28-year-old has made seven appearances, just three in the Primera Division, since joining the European champions from Levante last summer.
He is a reported target of Premier League sides Arsenal and Liverpool but told??Spanish sports newspaper Marca: “I feel very calm. Obviously, one always wants more.
“I’m not a conformist or someone that gives up easily. I know that the situation is not one that one would like but that is where I need to bring out the best in me and be stronger.
“It’s not the first time in my career that I’m in a position of being an understudy.”
Spain international Iker Casillas is Real Madrid coach Carlo Ancelotti’s first-choice keeper but Navas is determined to become number one in the future.
Navas, who started in Thursday’s goalless draw against Paraguay in an international friendly in San Jose, said: “I know what path I need to follow in order to obtain the results I want.
“For me it’s a privilege to be at Real Madrid and I try to prove day after day the reasons why they signed me.
“I have a great rapport with all my team-mates and the team welcomed me with open arms from the first day I got here. I have received the confidence that one needs in order to feel calm.”
Navas, whose crucial saves helped Costa Rica reach the quarter-finals of the World Cup in Brazil last year, is tied to the Merengue outfit until June 2020.