Jardim's Monaco led 1-0 at the interval thanks to Bulgarian striker Dimitar Berbatov, who found the back of the net with a diving header on the stroke of half-time at the Stade Jacques Chaban-Delmas.
But it went downhill in the second half as unbeaten Bordeaux moved top of the table, pilling on four unanswered goals courtesy of Diego Rolan's brace and penalties apiece to Emiliano Sala and Wahbi Khazri.
The result left Monaco winless from their opening two fixtures, with Evian TG only sitting bottom due to their inferior goal difference, and Jardim voiced his approval with referee Tony Chapron and his decision to award two spot-kicks.
"We had a game with two very different halves, a good half of Monaco where we were very well organised and a second half in which the adversary has come back and equalised quickly," said Jardim, who was appointed as Claudio Ranieri's successor in June.
"Then we had two refereeing errors that sealed the match and after that there's been no game. We must continue to work - we will continue to believe in these players.
"I have certainty that their game will get better and also certainty that there will be more mistakes. The French referees are good but there will be more mistakes in the future."
Bordeaux's second successive win helped them to the top of the table, level on points with Saint-Etienne.
It continues Willy Sagnol's fine start to life as coach of Bordeaux, who handed the former France international his first senior job at club level.
And the 37-year-old urged his team to take more risks after a timid opening half on Sunday, releasing the shackles to take charge against last season's runners-up.
"The Bordeaux of the second half is the one I'd like to see often, with players who take risks, who are trying, who are fun," Sagnol said.
"There Ligue 1 teams that are superior to us but we must keep that desire to do well and the desire to show a different image of Bordeaux."