City had 12 attempts at goal, five of which were on target, but Everton managed to hold on thanks to goalkeeper Tim Howard, who made several brilliant saves to deny Sergio Aguero and Raheem Sterling.
"We can't be worried after playing that way. It was very strange the team didn't score -- it's an accident that happens in football sometimes," Pellegrini told reporters on Friday.
The Chilean coach said teams often sought to frustrate City by keeping eight or nine players behind the ball, but this would not change his side's approach to games.
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"We must continue to play in the same way and trust we will score goals," he said.
City have suffered no fresh injuries following Wednesday's game although Fernandinho, Eliaquim Mangala, Wilfried Bony, Vincent Kompany, Samir Nasri and Patrick Roberts remain out and will miss Saturday's game.
"Probably one or two of the players will be fit next week," Pellegrini said.
City, who are third in the league and three points behind leaders Arsenal after 21 games, will hope to gain some momentum against eighth-placed Palace, having not won back-to-back league games since early October.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Toby Davis)
