With Harry Redknapp staying tight-lipped about reports linking him to QPR and the club’s majority owner Tony Fernandes keeping his counsel on Twitter, pressure is mounting on Hughes.
But the 49-year-old, who replaced Neil Warnock at the Hoops in January, insisted the Hoops do not need wholesale changes amid a relegation battle.
“Stability is absolutely what this club needs in the long-term,” he said.
“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.”
He added: “We’re at a point in time where we need to understand where we are. 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].”