Per BBC Sport, the French manager said it was Arsenal's responsibility but explained that Sanchez's absence was in no way a failure to cooperate:
"On Monday there was a lot going on, it is a special day for Alexis Sanchez—you have to do paperwork and travel. Was he still our player on Monday or not? You don't know.
"It is just a bad day for him to be tested. Honestly, on the administration side it would still be our responsibility because he had not moved. I don't know what really happened.
"I am quite relaxed because we have nothing to hide here, we always try our best to cooperate with doping control. The intention of Alexis was not to hide and we have nothing to hide."
Per the Guardian, "there is no suggestion of wrongdoing by Sanchez or the clubs" and it was merely an administrative oversight on Arsenal's part that led to the FA not being notified of the 29-year-old's absence from training, as is protocol.
After a protracted period of speculation, Sanchez finally left Arsenal to join United on Monday, with Henrikh Mkhitaryan moving the other way.
The Chilean has been included by manager Jose Mourinho in the Red Devils squad to face Yeovil Town in the FA Cup fourth round on Friday at Huish Park.
Sanchez could potentially make his Premier League debut for United on Wednesday, when they face Tottenham Hotspur at Wembley Stadium, while his first opportunity to play on the home side at Old Trafford will be Saturday February 3 against Huddersfield Town.