Nuno's popularity has hit a new low in recent weeks following his decision to leave out Alvaro Negredo and supporters at the Mestalla voiced their backing for the former Spain forward who was watching from the stands.
Valencia's victory lifted them to sixth but their erratic form in Spain's top flight and the Champions League has dampened hopes the Singapore-owned club can challenge for silverware this term.
Losing finalists in Europe's elite club competition in 2000 and 2001, Valencia are second in Champions League Group H, three points behind leaders Zenit St Petersburg, ahead of Wednesday's trip to Belgian champions Ghent.
"The fans want their team to win and to enjoy the way they play," Nuno told a news conference.
"I understand the supporters, it hurts me personally but I only have positive words for them," added the 41-year-old who is in his second season in charge.
Media reports have said Nuno was unhappy with comments Negredo made about tactics but he has underlined the decision to sideline him is "purely sporting".
Negredo, 30, joined from Manchester City in the close season for a fee of just under 30 million euros (£21.3 million) but has yet to reproduce the form that earned him 21 Spain caps, with his most recent appearance coming in November 2013.
He last played for Valencia in the 3-1 La Liga defeat at Athletic Bilbao on Oct. 4.
"I have already explained the Negredo issue in quite a lot of detail," Nuno said. "There is nobody who has a greater interest in seeing him return to help us than me.
"There are responsibilities. My technical team and I are doing work I consider very acceptable. We want him to return and up his game."
(Reporting by Iain Rogers, editing by Tony Jimenez)
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