The Dutchman's side are already out of the Champions League and League Cup, while they sit fifth in the Premier League, but goals from Wayne Rooney, Daley Blind and Juan Mata on Friday kept their hopes of a first FA Cup trophy since 2004 alive.
Van Gaal was thrilled with the way his team performed against their Championship opponents and talked up the importance of the competition after the match.
"The Premier League is very important but the FA Cup is the greatest cup in England with a long and important history," he told BBC Sport.
"We have not won it for a long time so we dream of it, but after two wins you can't say that we will win it. It [the performance] was maybe better than we had trained. We played at the right time against the resistance of Derby.
"We gave their goal away but at half-time I said that it was a good performance, keep it up and we will win - and we did."
The goal from centre-back Blind with 25 minutes remaining restored United's lead after George Thorne had struck for Derby in the first half and Van Gaal praised his player's desire.
"Blind's goal? You have to sniff it and he sniffed it," said the manager. "It was a great goal."
