After a drawn-out process, Valencia announced on Friday that Singapore billionaire Lim ha reached an agreement to complete his purchase of the club.
And Valencia celebrated the news in style as they accounted for Elche 3-1 at Mestalla courtesy of strikes from Shkodran Mustafi and Dani Parejo, and David Lomban's own goal.
Speaking post-game, Nuno said Valencia - third in the table - will get stronger under Lim's ownership.
"The team played a really focused, competitive game," said Nuno. "We have to approach the goal like we did. We had good moments and we played a good game.
"Peter Lim came down before and after the game to congratulate the players. He was also at the hotel. This was a very important moment for us. Mestalla had an incredible atmosphere. We love playing at home.
"Valencia will be stronger every day with Peter Lim. We're a club that's on the right track, although there's still a lot of work ahead of us."
Nuno added: "It was important to win in this fashion, it was a fair victory. We worked really hard over the full 90 minutes. Elche didn't make winning easy.
"We neutralized their strengths, but they wouldn't allow us to use our counter-attack. Fran Escriba has been doing a great job for quite some time. They didn't give us a single opportunity."
Saturday's triumph also saw star loanee Alvaro Negredo make his long-awaited debut, the striker having broken his foot before departing Manchester City.
Negredo played the final 10 minutes and the Spain international was overwhelmed by the supporters' ovation.
"This was an important win, I'm very happy to be back. It's been three very hard months. Now I need to find my rhythm and find my place in the team," Negredo said.
"I was very excited to play. In the morning, I was like a kid and as the day went on I started to relax. These have been three very hard months and I appreciate everyone who has worked with me in my recovery, both in Manchester and here.
"The ovation from Mestalla made my hair stand on end."
