Goals from Ander Herrera, Marouane Fellaini and Wayne Rooney booked United’s place in the last eight with a 3-1 win at Preston North End in the fifth round on Monday.
The third tier team took the lead early in the second half through Scott Laird but van Gaal’s side ultimately proved too strong.
Their reward is a potentially classic home tie against Arsenal on the weekend of March 7 and 8 after three successive away ties against lower-league opponents.
“We have a draw at home, which is important in FA Cup matches,” van Gaal said. “I am pleased we can play against Arsenal and at home.
“Every game in the FA Cup is difficult to win because every team is giving everything.
“You have seen it also in this round, how many better situated teams have lost so I don’t think that of course when you play against a lower team then the chance to win is always bigger.
“I am very happy we can play now against Arsenal and for the first time we play at home.”
United and Arsenal have both won the FA Cup on 11 occasions, with their last meeting in the tournament won by United in the last eight in 2011.
Arsenal’s most recent triumph came last season against Hull City, while United have not lifted the trophy since 2004.
– Shock lead –
Van Gaal admitted he feared for his side’s place in this season’s competition when Simon Grayson’s men went ahead through Laird.
Van Gaal’s response was to introduce Ashley Young and switch formation and it paid off.
“Of course, when we conceded a goal, we have to fight again for the victory,” he said.
“In the first half we didn’t create ourselves many chances so that is why I changed the shape. That was why I think we made the goals.
“I have to give to all the credit to the players because they have done again everything and the spirit in the team is unbelievable.”
After being relatively quiet in his role as a midfielder, Fellaini was moved further forward to partner Rooney in attack and the Belgian scored the visiting team’s second goal with what van Gaal described as a “fantastic training goal”.
Van Gaal said Fellaini offered United an alternative way of attacking when opponents became difficult to break down.
“I have used a lot of times already Fellaini, more than ever and he scores more than ever,” Van Gaal said.
“He is a player that when we cannot beat the pressure with quality, we can always beat the pressure. That is a quality.
“Now I have played him for the first time in his position but we have a lot of players who can play there.
“The whole team did it well because they believe also that we could do it with this shape
“As trainer-coach or a staff you can change the system but your players have to believe in it and perform it and that is not so easy and they do it and not for the first time. That is fantastic.”
Van Gaal also revealed Robin van Persie would be available to face Swansea in the Premier League on Saturday after the Dutch striker missed the match at Deepdale through injury.