Wolves took a point from their first game back in the top flight after a six-year absence, but they twice needed to come from behind against a team that played more than half of the match with only 10 men.
Last season's Championship winners have been tipped to challenge for a top-half finish in the Premier League this term, and Nuno is confident that his side will continue to improve throughout the campaign.
"We have character because we came back from a goal down twice, which is not easy," he told BBC Sport.
"Today taught me that we can react to goals but we have a lot to improve. We have always known we have quality but we are in a growing process. It was the first time for a lot of us in the Premier League but we will get better and better.
"It was a good atmosphere and the momentum must go on, everybody has to believe. We can only control our own expectations and the fans must enjoy.
"It was a team effort. Raul [Jimenez] scored the equaliser but I think the reaction from the team and the desire was always us - that requires energy and character. Everton reduced the space and they do not concede too many situations, but now it is our job to find solutions."
Wolves' second match back in the Premier League will see them take on Leicester City next weekend.