The Capital One Cup winners were beaten 2-1 by the Latics at the Etihad Stadium to crash out of the competition they lost in the final to the Championship last season.
In the wake of the defeat, former City and Leeds United midfielder Mills told Sky Sports News Radio that perhaps Pellegrini went into the contest with some complacency which lead to the side's downfall.
"It should have been a comfortable victory for them. You have to give Wigan credit. They had a game plan, they played very well, but City at home, this should have been a banker for them," said Mills.
"They gave it a real good go in the last 20 minutes but didn't really create too many clear-cut chances and really test the goalkeeper.
"He (Pellegrini) may well have got it wrong. He has to take a lot of responsibility. When you play against a lower-division side you know they're going to work hard, you know they're going to be organised.
"He's had one or two problems so far this season against lower-division teams. He probably went into the game thinking 'I've got more than enough to beat a Championship side' but you have to question his decisions with the mistakes that led to the two goals."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball