The Saints took a first-half lead through prolific Ricky Lambert, with the striker heading past Hoops keeper Júlio César, before Jason Puncheon extended their advantage in the 43rd minute.
Junior Hoilett did offer QPR brief hope with a goal early in the second half but the Hoops were poor throughout the game, dubbed ‘El Sackico’, and a miserable display was compounded by Anton Ferdinand’s late own goal.
QPR’s majority shareholder has previously backed manager Mark Hughes after recent disappointing results, but Fernandes admitted he felt “gutted” about the defeat by the Saints.
“I have put my heart and soul into this with my other shareholders,” Fernandes posted on Twitter.
“And done all we can to give support to players and all management. I can only apologise to the QPR fans. We keep fighting.”
In a later post on Saturday night, he added: “Let me tell you fans come first. Everyone including me let the fans down. Many of us need a hard look at ourselves. QPR has amazing fans. They deserve better.”
Meanwhile, Hughes, who is currently the favourite to become the first Premier League manager to be axed, insisted he would not walk away from the club.
“The club needs stability. Maybe this is a watershed moment as we can’t get much lower. It’s my intention to see it through,” said Hughes, whose side are rooted to the bottom of the table.
“I knew this job was going to be problematic. I was quite prepared to raise expectations as I thought we’d have a good season.”