Pellegrini has come in for criticism after City's Premier League title prospects were hit by a 3-2 loss at leaders Liverpool and a 2-2 home draw against Sunderland.
Those results leave City nine points behind Liverpool and although they do have two games in hand, they must now rely on other results going their way.
With another Premier League title looking unlikely, Mills said that Pellegrini should not take all the flak.
"It's very, very difficult to point the finger at one person," Mills told Sky Sports Radio.
"The players are the ones that cross the white line, have to go out and play. The manager sets the mood, sets the tempo, sets the tactics, everything else. It's a little bit of both.
"Sometimes there is no reason (for a late collapse). Look at Sunderland, fighting for their lives, pulled off a fantastic result (on Wednesday).
"City's last couple of results haven't been (great). It's going to be difficult for them.
"At one point you looked at Manchester City and thought 'well, it's in their hands, they can win the league no problem'. And suddenly now, they're up against it to finish second."
City can ill afford another setback when they host struggling West Brom on Monday.
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