Mauricio Pochettino's side claimed a share of the spoils at the Santiago Bernabeu, with Madrid unable to capitalise on some good chances after Cristiano Ronaldo's penalty had cancelled out a Raphael Varane own goal.
Spurs goalkeeper Hugo Lloris made two outstanding saves to deny Ronaldo and Karim Benzema in the second half, but Navas was also called upon to prevent Harry Kane from snatching all three points for the visitors.
The Costa Rica international was frustrated Madrid could not make it three wins from three in Group H but felt luck was not on their side.
"We can't leave satisfied," he told Antena 3 , as quoted by Marca . "We wanted to win, but thanks to God we were able to do our job well.
"They had opportunities and we did too. It was a good game.
"Lloris made big saves, we had chances but the things we tried didn't go the way we wanted. We always want to keep a clean sheet, but there are situations we can't control.
"Hopefully in the future we can avoid conceding a goal and manage to record the victory."
Madrid and Spurs are level on seven points and with exactly the same goal difference heading into the return fixture at Wembley in two weeks' time.