Mills has also questioned the hunger and form of midfielder Yaya Toure, whose future beyond the end of the season has been the subject of speculation.
City have suffered two damaging defeats in the Barclays Premier League, to title rivals Leicester and Tottenham, since it was announced Guardiola would succeed Manuel Pellegrini as manager in the summer.
Mills, 38, who made 54 appearances for City between 2004 and 2006, wrote in his Sportlobster blog: "I believe the City players have been hugely distracted by the Guardiola announcement and they've taken their eye off the prize.
"Yaya Toure knows he's not going to be around next season and his hunger and desire has been questioned.
"They are still in four competitions so they may still be successful and the announcement of Pellegrini's departure could've gone either way in terms of the effect on the squad but two home defeats, albeit to top four opposition, indicates to me that not all is well at the Etihad."
Source: PA