Mourinho was referring to Malaga's Chilean coach Manuel Pellegrini, whom he replaced at Real at the end of last season after leading Inter Milan to a treble of European Champions League and Italian league and cup.
Pellegrini returns to the Bernabeu for the first time since he was sacked when Malaga play Real later on Thursday and city mayor Francisco de la Torre said he would be delighted if his team upset the La Liga giants.
"With those statements he (Mourinho) wanted to affect Pellegrini, hurt his feelings as a coach and also indirectly the Malaga players, but it seems to me an error of judgment," De la Torre was quoted as saying in local media.
Mourinho had been "clumsy" and his behaviour had not done Real Madrid any favours, De la Torre said.
"I would be delighted if we beat Real Madrid, it would give me more pleasure than ever," he added.
The outspoken Mourinho has ruffled feathers since he arrived in the Spanish capital.
He has repeatedly complained about La Liga referees, clashed with Real Director General Jorge Valdano and accused those who set the match calendar of favouring Barca.
Pellegrini refused to rise to Mourinho's bait, telling a news conference it was an honour to coach Malaga, especially as he had been given the task of saving the Andalusian club from relegation.
"Everyone has their way of behaving," he said. "I did not hear or read what he (Mourinho) said, nor will I reply.
"I know what it means to coach Real Madrid. Last year we tried our best, respecting the values of the institution."
