Pep will be responsible for this, therefore he did not leave Man City and is ready to prove everything. Pep will not let this losing streak continue.
The manager is always the one who feels the most pressure, the players cannot be sacked, but the manager can, i am not saying that there is any chance in hell that Pep gets fired, but he has a lot of work to get his serial winning team back in hunting mood.
I don't think we should blame Pep for this. Much of Man City's troubles stem from an injury crisis, including the loss of Rodri in September. Kevin De Bruyne, Ruben Dias, John Stones, Manuel Akanji, Nathan Ake, Jeremy Doku, and Jack Grealish have also been absent at key times. You have to accept that. You can't blame each other.
Yes you are right, all of those are the main factors that have caused Manchester City performance decline lately and also added to by some pressures within the team management related to the problems that are befalling them, this decline is natural condition but they still have to resolve it immediately and get back on the right track.
Pep job is only to work by correcting every mistake and really restoring the players confidence because besides that efforts to improve the line-up and find replacements for injured players can only be done when the transfer window has opened.