The club's owner approved a huge summer outlay in the transfer market and has consistently supported his manager in public despite the side's failure to win a league game this season.
But a 3-1 home defeat to Southampton, who had not previously won a point on the road, prompted a change of tone from Fernandes.
He tweeted: "I feel gutted. I have put my heart and soul into this with my other shareholders and done all we can to give support to players and all management. I can only apologise to the QPR fans. We keep fighting.
"Let me tell you Fans come first. Everyone including me let the fans down. Many of us need a hard look at themselves. QPR has amazing fans. They deserve better."
Hughes did not try to disguise the shortcomings in his side's performance against Southampton, calling it the worst of his 10-month reign.
But the Welshman insisted he would not be resigning, saying: "I don't run away from challenges. This is a huge challenge. It was a huge challenge in January when I undertook it.
"There weren't too many people queuing up when I decided it was the right role for me. I knew it was going to be problematic. We all understood that.
"This year we obviously had real expectations and I was quite prepared to raise expectations because I thought we would have a good season. It hasn't quite happened, unfortunately, and because we have raised expectations more people are disappointed."