The Costa Rica international played the full 90 minutes as Real succumbed to defeat in Warsaw, goals from Mario Gomez and Marcos Alonso giving Fiorentina the victory after Cristiano Ronaldo had opened the scoring for Carlo Ancelotti's men.
But the 27-year-old stressed that he felt good throughout his first appearance for Real and insisted that he is not at the club to cause controversy as he competes with Iker Casillas to be first-choice goalkeeper.
"Unfortunately, we couldn't get the win, but I felt good and the team leaves feeling good," Navas said.
"The first time out with my new team-mates is important. We need to keep working and improve every day.
"I'm very calm, I'm not here to do wrong by anyone. I humbly come to work every day to work hard, as I've done very day of my life.
"I'm available whenever then coach needs me, I won't hang my head and I'll work hard every day."
Real now take on city rivals Atletico Madrid in the first leg of the Supercopa de Espana on Tuesday and Navas is understandably determined to claim his first trophy with Ancelotti's side.
"Now we have to think about the next game," he added.
"We want to win and have a winning mentality. The team is very motivated, we know it's a major title and we'll fight to win everything."
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
