QPR's home defeat - which saw fans chant "you're only here for the money" at certain players and cheer when summer signing Jose Bosingwa was substituted - has left them as the only team in the four English professional divisions without a win.
They are four points adrift of 19th-placed Saints.
Fernandes was not at Loftus Road, where fans also waved placards calling for Harry Redknapp's appointment, but tweeted: "Everyone including me let the fans down. Many of us need a hard look at themselves. QPR has amazing fans. They deserve better."
In his role as a pundit on Match of the Day, former Spurs manager Redknapp said: "Mark’s still in the position, he’s a top bloke and an excellent manager.
"He knows what he’s about and until there’s a change, if there is one, then it would not be fair for me to discuss it."
Fernandes is not due back in the country before next weekend's match against Manchester United at Old Trafford, but is reported by the Daily Mail to be considering flying in to change his manager.
Hughes claimed on Friday that his big-name players had the stomach for the fight and that, when injuries abated, they would fly up the table into the predicted top-half finish.
However he has now changed his tune after bringing on a pair of players who helped the Rs win promotion - Jamie Mackie and Shaun Derry.
"We're at a point in time where we need to understand where we are," Hughes said. "We're not talking about a successful mid-table finish now because, given the manner of the performance against Southampton, we are in danger of going down.
"We have to recognise that, we have to get the right mentality to move us forward and maybe the right players. I take responsibility for that and, given the performance, I picked the wrong players [against Southampton]."
He naturally believes that he is the right man to lead the West London club forward.
"Stability is absolutely what this club needs in the long-term," he added.
"Until you get to that point where you can establish yourself in the Premier League, then you have to go through periods where there is doubt or apprehension about what the future holds.
"We are at that point in time now, but I think wholesale changes once again for this club would be the wrong decision in my view. You would expect me to say that but I honestly believe it.
"The owners understand that we're at that place in time. We just need to get through this, come out the other side and look back at this and think, 'We needed to go through that period to grow stronger'.
"It is difficult for everybody at the moment but we're not going to run away from it."
After narrowly avoiding relegation on the final day of last season, Hughes vowed that QPR would not find themselves in another fight for survival again under his leadership. Those words have come back to haunt him.
He has not been helped by a Twitter spat between striker Djibril Cisse and a fan.
"Come to the training ground, we’ll have a chat big man," the Frenchman responded to criticism.