Pellegrini coached Madrid for one season following the return of Florentino Perez to the club as president and a substantial investment in the playing staff.
Despite the huge outlay, which saw the likes of Cristiano Ronaldo and Kaka join in big-money deals, Pellegrini was unable to win a trophy and was replaced by Mourinho in the summer.
"I have nothing to prove and I don't want comparisons (with Mourinho)," he said. "The past has no relation to this new project."
Pellegrini, who has taken over with Malaga in the bottom three following a miserable start to the season and three defeats in the last three games, was attracted to his new post by the long-term ambition of the club.
"It's a project with a big future and to be part of that is attractive," said the Chilean, who replaced Jesualdo Ferreira at the helm following his sacking earlier this week.
"We will see what we can do to improve - we have an immediate need to turn things around."