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The Andalusians saw off the recently promoted side with a late effort from Olinga, who became La Liga's youngest goalscorer with his 83rd minute strike.
Speaking to the press after the game, the club's Chilean coach admitted that he would have settled for a solitary point given the performances of both sides.
“We were fortunate enough to win, whilst a draw on that last play would not have been unfair," the 58-year old opined.
Los Boquerones have been subject of much upheaval following financial difficulties at the club, and Pellegrini believes his side did well to put this and the departure of several star names behind them.
"Our group has been through some very difficult times but they have served to make them stronger in spirit and mind," he concluded.
Malaga's next fixture is their Champions League play-off match against Panathinaikos on Wednesday.