Alongside Mourinho, the former Porto goalkeeper was at the club as they claimed the 2003-04 UEFA Champions League.
Nuno, who was appointed in July, said he was grateful for the opportunity to see one of the world's best close up.
"To have a chance as a player to work with one of the best managers in the world and at the same time, not work but be focused also on the work that he does and try to understand each day the why and the how he does it, it's a big influence," he told a news conference on Friday.
"It was important because in those moments we achieved big things in Portuguese football.
"I now understand the things that he did back there [at Porto], and the good things I'll try to apply, and the bad things - because everybody has them - I'll try to take them away.
"Every coach in my life as a player has a big influence in my decisions now."
Valencia finished a disappointing eighth in La Liga in 2013-14, and Nuno said the aim was to return to the UEFA Champions League.
"Our main goal is to achieve the Champions League next year. We know it's going to be hard, very hard because we're going to fight against big clubs," he said.
"But Valencia is a big club, and in our history, it's the first time in 10 years that we've been out of Europe, so we must get there as soon as possible. This is our main goal."
Asked if La Liga was the strongest league in the world, Nuno had "no doubt" it was ahead of the Premier League.
"With all my respects to the Premier League, I think the Spanish league at the moment is the most competitive with the best players in the world out there," he said.
"Every game is a big one. You cannot ever predict a result. So I think it is the best league in this moment."
