Fernandes had given United an early lead from the penalty spot at Old Trafford but Jose Mourinho’s side battled back and led 4-1 by half time.
United were reduced to 10 men before the break after Anthony Martial was dismissed for his swipe at Erik Lamela, while Jose Mourinho’s side wrapped up their win with two goals in the second half.
Fernandes, meanwhile, was substituted at half-time after struggling to make an impact in the opening 45 minutes.
And following the loss which has left United with just three points from their opening three Premier League games, Fernandes admits he and his teammates need to improve quickly.
‘Represent this big football club as we did today is not enough,’ Fernandes wrote on Instagram.
‘We apologise to all the fans for this big loss at our home.
‘Time to bow our head, reflect and do much more for us, the club and fans.’
David De Gea also issued an apology to United fans on Twitter: ‘We feel exactly like you. No excuses. Sorry’
Marcus Rashford was the first United player to issue an apology to fans after the loss.
The striker admits he felt ‘horrible’ after United were beaten by Mourinho’s men.
‘First and foremost I’m a United fan,’ Rashford posted on Twitter.
‘This is my club. I’m so proud to wear this shirt but there are no excuses, it’s just not good enough and to every single fans around the world that tuned in today, I’m just so sorry.
‘I would have stayed away from social media tonight but you deserve to hear from me during the highs and the lows, there is no hiding.
‘I feel horrible but I promise you we will do better.’