City are only three points off the top of the Premier League going into this fixtures but, following defeats at Cardiff and Aston Villa, Redknapp believes Pellegrini would already be coming under pressure from the media were it not for the poor start made by Manchester United.
Redknapp said in his blog for Sky Sports: "Pellegrini's naivety in only playing two central midfield players against Bayern Munich in the Champions League was surprising and his inability to address the problem while the best team in the world were all over them was concerning.
"Their domestic away form has also been poor. When you look at City's squad and all the quality that's there and see them throwing away leads and losing to Cardiff and Aston Villa, that tells you something is wrong.
"Of course, senior players need to take some responsibility because they should be pulling people up if they are getting lax or complacent.
"But fundamentally it comes down to the manager and it's been a strange start for Pellegrini.
"Their victory over Manchester United was one of the best I've seen for three or four years, but in losing games which they could have won comfortably they have shown they are much more open this season than they were under Roberto Mancini.
"That's something Pellegrini needs to look at; in some games he will need to get an extra midfielder in there and say to Sergio Aguero, Edin Dzeko or Alvaro Negredo they may not start in some games.
"It's not easy but that's the problem you have when you have an abundance of riches."
Redknapp believes that City could find it tough at Upton Park on Saturday evening, particularly if West Ham score first - and he is looking forward to seeing Ravel Morrison in action again.
"West Ham's 3-0 win at Tottenham before the international break will be a real boost for them and, with the brilliant atmosphere there, the first goal is going to be crucial," Redknapp said.
"West Ham set up with no forwards at White Hart Lane, with Ravel Morrison, Ricardo Vaz Te and Mohamed Diame playing up front.
"That worked so well for them because they could soak up pressure, use their strength at set pieces to get ahead and then hit Spurs on the counter-attack when the home side went looking for the equaliser.
"And if West Ham can score first on Saturday then City could be facing a real problem.
"It will also be a big night for Morrison, who is making plenty of headlines at the moment - and for the right reasons.
"We've got three players coming through for England now who are the most exciting talents we've produced in a long time: Morrison, Ross Barkley and Andros Townsend.
"The common denominator is something we don't have enough English players doing - they can all travel at genuine pace with the ball.
"All three dribble with their left and right and it makes you twice the player if you can do that.
"When you can dribble with either foot it makes you so difficult to defend against. As a defender you don't know whether to show them left or show them right; it's such a talent to have and gives you a different dimension.
"Morrison's excellent solo goal against Tottenham showed what he can do and we all know he's a genuine talent. There will be bumps in the road for him, though, and he needs good people around him.
"But Sam Allardyce has done a good job with Morrison, after Lee Clark got the ball rolling for him at Birmingham last season, and the penny appears to have dropped for the former Man United youngster."