Goals from Angel Di Maria, Ander Herrera, Wayne Rooney and Juan Mata secured an emphatic success at Old Trafford and enabled Van Gaal to celebrate a first competitive win as United manager.
The game served as a perfect illustration of the attacking talent now at United's disposal, with Di Maria particularly impressive on the day Colombia striker Radamel Falcao made his debut as a second-half substitute.
United fans are eager for their side to challenge at the top of the Premier League following a hugely disappointing seventh-placed finish last term.
However, Van Gaal is more focused on developing the team's identity in his first season at the helm.
"Our purpose and our goal is to be in the first three because we have to qualify ourselves in the Champions League," Van Gaal said.
"The most important thing is the trajectory; we are building a process and we have to play in a certain style."
Di Maria, who arrived from Real Madrid for a British-record transfer fee of £59.7 million, was heavily influential before coming off with cramp in the closing minutes of his home debut.
The Argentina winger was unquestionably United's man of the match, yet Van Gaal was not completely satisfied with his showing.
Van Gaal added: "When you prepare three goals and you make the first goal by yourself, then you cannot play bad but he had a lot of unnecessary losses [of possession] I think."
