Ole Gunnar Solskjaer’s side ended the season in sixth position, five points adrift of a Champions League qualifying spot having lost six out their final eight matches.
Sanchez, meanwhile, struggled to make any sort of positive impression, managing just two goals in 27 appearances.
The Chile international suffered an injury during United’s draw at Huddersfield last weekend but was present at Old Trafford for the traditional end of season lap of appreciation.
Earlier on Sunday it was reported that Solskjaer’s squad had been divided over the bonuses awarded to the likes of Sanchez and Paul Pogba, but the former Arsenal forward appeared to hit out at those suggestions.
He wrote on Instagram: ‘It was a very tough season…the fan (sic) are the ones who deserve an apology as they always support you no matter what happens.
‘Personally, I didn’t perform as much as I was expecting because of unpredictable injuries.
‘Press and people were speculating of things that were not even true. I was always a professional in all aspects.
‘I apologise to the fans for not being able to achieve our goals, Nevertheless we are Manchester United!
‘Players and staff are questioning if we were doing the right thing and if we were giving our best for this football shirt.
‘I’m certain that Manchester United one day will return to be the club, as it was in the old days with Mr. Alex Ferguson.’