Sanchez joined United in January as part of the deal that took Henrikh Mkhitaryan to the Emirates Stadium.
The Chile international arrived with a reputation as one of the best players in the Premier League, but managed just three goals in his 18 appearances for United in the second half of the 2017-18 campaign.
Sanchez has conceded that it has been tough for him since arriving, but the attacker is confident in his future at the club.
"I think that in every game I've played in I've maybe found it hard to adapt to the style of play and I've been getting to know my teammates," Sanchez told the FA Cup matchday programme.
"I believe that United really is a very big club on a worldwide scale and even more so in England where it's the biggest. They always want to win and to be fighting on all fronts and that's the reason I wanted to come here.
"I also had some great players alongside me at Barcelona, some highly experienced guys who had great quality. I think that United are not too dissimilar as a club to them in their size and stature.
"However, we still have areas where we can improve, and we can do this day-to-day and a game-to-game basis. I believe we need to improve in all aspects."
United suffered a 1-0 defeat to Chelsea in the final of the FA Cup on Saturday night.