Sergio last month became Cluj's 16th coach since 2001 after Andone, who led the Transylvanian side to their third league title last season, left by mutual consent.
"I can't be pleased with what is happening in Cluj," Dumitru Dragomir told local media ahead of Cluj's home clash with Braga in the Champions League on Tuesday.
"I think these guys were stupid (to replace the coach). It was another hasty decision, they have done this in recent years too."
Cluj are third in Champions League Group H, battling for the second qualifying spot with Galatasaray and Braga. Leaders Manchester United are already assured of a last 16 place.
"I think that the team would have looked much better, even in the Champions League, if they had kept Andone," said Dragomir.
"They're a completely different team, with a different attitude, with him."
The much-travelled Andone, who previously coached another eight Romanian clubs as well as being at the helm of teams in Cyprus, Saudi Arabia, United Arab Emirates and Bulgaria, was criticised by local media and fans for Cluj's domestic performances.
Cluj are sixth in the Romanian league standings with 25 points from 16 matches, 16 points behind leaders Steaua Bucharest.