As the club's new manager faced the media for the first time at Old Trafford, Van Gaal said he has realised within two days the magnitude of the club and the size of the task ahead of him.
The 62-year-old said: "I will do my utmost in my first season – that's what I can give.
"This is the biggest club in the world. Within two days I know already how important Manchester United is, but also how important the supporters are.
"It's the biggest club known worldwide, but in sport you are never the biggest club because every season you have to prove that and last season we were seventh.
"I cannot give predictions because you never know. No one predicted the Dutch team would come so far at the World Cup. Nobody predicted German would beat Brazil 7-1, or that the Dutch would beat them 3-0.
"I have to work, I have to prepare a team and adapt to this big club. It will not be easy but I will do my best. When you see my career, what I have won, that is as much as I can say. The future shall show if I can do that again.
"The owners and the CEO have a lot of confidence in me. It was because of this that they have come to me, and I explained my philosophy which made them excited.
"There is a lot of expectation both from them but also the fans, who are very important, but also because of that this is a great challenge, and that is why I chose this club. I hope I shall fulfil the expectation, but it shall be difficult."
Van Gaal, who took Netherlands to a third place finish at the World Cup this summer, dismissed the idea of a break to take immediate charge at Old Trafford.
He arrived in Manchester on Wednesday, just four days after his Dutch side beat Brazil 3-0 in Brasilia, and oversaw the second half of a double training session before taking the first-team through their paces in earnest on Thursday.
Van Gaal was shown around Old Trafford by Sir Bobby Charlton and the former Barcelona, Bayern Munich and Ajax boss spoke of his pride at being lead through his first steps by United's most revered former player.
"I want to thank Sir Bobby Charlton – it was a great honour to come into this stadium and to be guided through my first steps as head coach by him.
"I was very proud to do that with Sir Bobby. I have the age to have seen him play so I know what he means for the club and English football."