The Argentine defender joined Manchester City from Atletico Madrid this summer but has borne the brunt of heavy criticism from City fans.
Demichelis was first ridiculed for his performance in a crucial Premier League clash with Chelsea, before being sent off at a key stage in Man City's Champions League tie with Barcelona.
But Xavi feels the 33-year-old offers something different in defence: technique and ability on the ball.
It is for this reason that Xavi feels Pellegrini brought the Argentine to the Etihad Stadium, something he thinks shows why the City boss is such a good coach.
"Pellegrini is a fantastic coach, with the way in which he wants to play football right from the back," the Barcelona midfielder told Jamie Carragher in an interview for the Daily Mail.
"For example, he has brought in Demichelis. He has been criticised but he can bring the ball out well from the back in order to get the team playing football.
"He has plenty of good footballers to play a passing game. But it’s another thing when they come up against Barca as we have seven or eight players of our own who hardly ever give the ball away."
Barcelona will have a two-goal advantage when they host Manchester City for the second leg in Spain, although their recent 3-1 defeat to Real Sociedad in La Liga might offer Pellegrini's side some hope.
First, though, City will have to overcome another set of champions: Wigan Athletic, last year's FA Cup winners - who they face this weekend.
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