Ole Gunnar Solskjaer's side finished sixth, but picked up just two Premier League wins from the eight games since the former Molde coach was given the job on a permanent basis on 29 March (AEST).
Sanchez has been a source of much frustration for United fans following his move from Arsenal in January 2018.
And the Chile international, who has scored just one league goal this term, took to his Instagram account to acknowledge that his performances have not been up to scratch.
"It was a very tough season, the fans are the ones who deserve an apology as they always support you no matter what happens," Sanchez wrote.
"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."
Whether Sanchez will be part of the United squad moving forward remains to be seen, with it seeming increasingly likely that the club will look to cash in on the 30-year-old in the close season.