The Spain forward signed a season-long loan deal at Valencia earlier this month, with the Liga club having the option to make the move permanent.
Negredo is still recovering from the broken metatarsal he suffered in July and Pellegrini revealed on Friday that he was not in his UEFA Champions League plans.
"The decision for Negredo to go was very important," Pellegrini said.
"We have a restriction on the players we can use in the Champions League. Alvaro Negredo was injured. He wasn't going to be on the list.
"He wanted to go back to Spain. It all starts from the restrictions due to the money we spent.
"It is one striker less of course, but we have Edin Dzeko, Sergio Aguero, Stevan Jovetic and other players we can use behind the strikers. There are other options."
City visit Arsenal on Saturday as Premier League action resumes and Frank Lampard and Eliaquim Mangala are in line for club debuts.
Veteran midfielder Lampard, on loan from New York City, and defender Mangala, who cost City a reported £32million from Porto, add significant strength to Pellegrini's squad.
"Frank is ready," Pellegrini added.
"He has worked for about one month and he doesn't have any problems.
"Mangala is working normally and is in the squad list also. We have to play three games in a week so we will see if they play in these games.
"Both of them are ready to do it but I can't say which games they will play or if they will play."
Defender Pablo Zabaleta is available despite suffering a knock while on international duty for Argentina but Jovetic (hamstring) and Fernando (muscle injury) are both ruled out for the Emirates Stadium trip.
