The centre-back believes the Chilean coach can propel the Etihad Stadium outfit to success both domestically and in the Champions League after they beat CSKA Moscow on Tuesday
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A knee injury has limited the number of appearances Demichelis has been able to make but he has started three of the last four matches in all competitions.
Pellegrini managed the 32-year-old at Malaga and was quick to swoop for the central defender when he arrived in the Premier League, with Demichelis confident the Chilean can bring success to the club.
"He can find a way to win," he told reporters.
"He has a way of making sure his teams play in the way he wants, that we play effective football and that we can challenge for important things.
"We are in a good place now and we will have to see what happens afterwards.
"It's clear that City have players who unsettle the opposition, players who in any moment, in any yard of space, in any action, can score a goal. It's a big worry for our opponents."
Victory over CSKA Moscow on Tuesday saw City qualify for the Champions League knockout stages for the first time in their history.