The Chile international officially completed his move to Old Trafford on Monday in a deal which saw Henrikh Mkhitaryan join Arsenal.
Chelsea were linked with Sanchez when United were in the advanced stages of the transfer.
But according to Conte, the 29-year-old, who is now the highest-paid player in the Premier League, was always out of reach for the Premier League champions.
‘We never were in this race. Ever,’ admitted the Chelsea manager.