Ruben Neves and Raul Jimenez twice levelled for the hosts, who competed an entertaining draw at a buzzing Molineux on Saturday evening.
Instead of buckling once behind, Wolves showed their character throughout the 90 minutes which will bode well for the coming nine months according to Nuno.
“We have character. We came back with a result two times, it’s not easy,” he said. “Having the strength to react to the moments we’d made mistakes taught me a lot.
“The quality is there. We over-played some moments but it’s natural when we’re growing. It was the first time for a lot of us in the Premier League, so I think we’ll get better game by game.
“It was the first game and we reacted well but have a lot to improve.”
Wolves were backed by tremendous support throughout the 90 minutes, which Nuno believes played a massive part in earning a point against the Toffees.
“We thank the crowd, Molineux was incredible - buzzing. It was a good atmosphere, but the momentum must go on, everybody must believe in what we do and what we want to achieve.
“The fans must enjoy it. I hope they enjoyed the team today and I must be humble and ask them for support at Leicester and here at Molineux next time.
“We can’t control the outside. What we have to do is control our own expectations, we’ll work game by game.”
Although Neves and Jimenez both found the back of the net, Nuno insisted it’s the team who deserve plaudits, rather than individuals.
“It’s a team effort. Raul scored but people could see the desire, the hunger of the team to put the result back and go for the win.
“Everton reduced the space, they didn’t concede too many situations. It was always us running and chasing, that requires a lot of energy and character.”