The Dutchman, smiling and looking relaxed after arriving from his stint as Netherlands manager at the World Cup, also made clear that the commercial demands at United would make his job harder.
"I'm now two days here," Van Gaal told reporters. "I've met a lot of people, and when you see that kind of people loving the club they expect a lot of me.
"Can I fulfil that expectation I think I can, but because of the greatness of this club it is much more difficult than in another club.
"This club is also guided in a commercial way and we have to fulfil that also, but it is not always possible to fulfil both.
"I will do my utmost best. That's what I can give. I cannot give predictions."
The former Ajax, Barcelona and Bayern Munich coach added: "I cannot give predictions because you never know.
"It's the biggest club in the world. Within two days, I know already how important Manchester United is, but also how important the sponsors are.
"I have to adapt to this big club. It will not be easy, but you can see what I have won."
The 62-year-old coach has been asked to make United a force again after last season's disappointing campaign under David Moyes. They finished seventh in the Premier League and failed to secure European football.
But Van Gaal's early double reference to United's sponsorship imperatives is likely to intrigue and alarm supporters.
The club is saddled with approximately $600 million in long-term debt following the takeover by the Glazer family, and the inference to be drawn from Van Gaal's comments is that he fears the club's commercial pressures may compromise the footballing priorities.
United, who this week announced a record kit deal with adidas worth $130 million a season for 10 years, have added England defender Luke Shaw and Spanish midfielder Ander Herrera to their squad this summer for a combined cost of 56 million pounds ($95.75 million).
Van Gaal said he had approved their signings from a list of transfer targets compiled by Moyes, but the Dutchman added that he would wait to assess the United squad before trying to buy more new players.
"First, I want to see the players performing my philosophy," he said. "Then, I will think about signing players.
"I want to look at the players here at present. I know the players, but I have not trained and coached them. It will take three or four weeks to see what they can do before we buy other players.
"Shaw and Herrera were already on the list and I approved them because I liked them."
Reports say the club covets at least one more midfielder and one central defender, in the wake of the departures of Nemanja Vidic and Rio Ferdinand.
Van Gaal guided the Netherlands to third place at the World Cup finals in Brazil in his second spell in charge of the national team.
He has previously won domestic championships with Ajax, Barcelona, Bayern Munich and AZ Alkmaar - including titles in his first season with Barcelona (1998) and Bayern (2010).
'CHALLENGE IS FIRST'
Asked what he would characterise as success in his first season at United, he said: "I don't know. First I need to see how quick the players can pick up my philosophy. I haven't worked with most of them so we have to wait and see.
"It's very important there is a click between the players and the manager. For me, the challenge is always first not fourth."
His reference to players and manager "clicking" was pertinent, since Van Gaal, while boasting many admirers, has also attracted a reputation as a disciplinarian.
But he said: "I'm democratic ... I am an empathetic human being."
When it was put to him that he could be seen as autocratic, he said: "That is unfair. The media wants to show that part of the personality.
"When you repeat that (idea), everyone thinks it is like that. Of course, I have a strong philosophy. (But) Sir Alex Ferguson has also a strong philosophy and he won a lot of titles."
Van Gaal said Ferguson - the Scot whose 26-year reign all successive United managers will be reminded of - had telephoned him to wish him luck.
"He called me to congratulate me and we have spoken about a cup of coffee," Van Gaal said.
"We know each other very well and I shall drink coffee and drink wine with him - maybe the better wine!"
Van Gaal - who said he hoped to find coaching roles for former United players Paul Scholes and Phil Neville, as well as Nicky Butt, who is already working with the squad - took his first training session on Wednesday.
But he will get a chance to analyse the current players in detail when they fly to the United States on Friday for a pre-season tour.
His debut as United manager will be against Los Angeles Galaxy on July 23.