City's 2-0 win over Wolverhampton Wanderers later that afternoon means that the two clash in a title showdown next Monday, with Nani anticipating a strong response from his side.
"There is anger from the players because we wanted to win [against Everton]," Nani told MUTV.
"We have to keep believing in our qualities because we still have a great opportunity to win the title. It's a huge game.
"It will be a difficult game, but if you want to win the league you cannot think about the atmosphere or the opponents. Of course [we can win]."
City boss Roberto Mancini earlier claimed that United are still favourites for the title.