Juan Mata scored twice in Sunday's Premier League game, either side of a red card for home captain Steven Gerrard, and despite Daniel Sturridge hitting back, Liverpool fell to a first loss in 14 league matches.
Victory strengthened United's grip on the fourth and final Champions League qualifying berth, with Liverpool now five points behind and Southampton and Tottenham Hotspur a point further back, leaving Van Gaal to reflect on a potentially decisive afternoon.
"It is the moment we are coming back and we beat Liverpool again," said the Dutchman, whose side had condemned Liverpool to their last defeat with a 3-0 win at Old Trafford in mid-December.
"We beat them again with their own weapons and the pressure on the ball.
"Now the gap is five points ahead of Liverpool and six ahead of Tottenham and Southampton, so the moment to win is one of the most important in my career."
Mata's superb performance in United's 3-0 defeat of Tottenham meant that he held on to his place despite Angel di Maria's return from suspension and he rewarded Van Gaal's faith with a fine display.
His 14th-minute opener saw him run on to a pass from Ander Herrera and beat Simon Mignolet with his right foot, while his second goal on the hour was sublime -- an acrobatic scissors kick from Di Maria's clipped pass.
Mata has struggled to hold down a first-team place this season, but Van Gaal offered a glowing assessment of his current form.
"Now he is playing as a false right-winger and the combination with Herrera and (Antonio) Valencia gives him more opportunities, so I am very pleased," Van Gaal said.
"I think he was one of my most constantly playing players, also in the beginning of the season, so I am not amazed, but I am very happy with him."
- Big challenge -
Gerrard apologised in a television interview for his dismissal, which came just 43 seconds after he had replaced Adam Lallana at half-time.
The former England captain, who recently returned from a hamstring injury, reacted to Herrera's sliding challenge by slyly stamping on the Spaniard's calf, prompting referee Martin Atkinson to brandish a straight red card.
Liverpool manager Brendan Rodgers admitted that Gerrard had been "probably a little frustrated" about having to watch the first half from the bench, but he refused to condemn his California-bound captain, who will join the Los Angeles Galaxy at the season's end.
"I won't criticise him because he's been brilliant in my time here," Rodgers said
"Sometimes these things happen
We'll move on."
Rodgers also played down an incident at the death -- moments after Mignolet had saved a Wayne Rooney penalty -- that saw centre-back Martin Skrtel tread on United goalkeeper David de Gea after chasing a through ball in vain, saying that it "looked worse in slow-motion".
Liverpool's defeat at Old Trafford proved the spur for a 13-game unbeaten run that revitalised their season and Rodgers urged his players to channel the frustration from their latest setback in the same fashion.
Asked about his side's chances of a top-four finish, he replied: "It's a big challenge
But when I looked at the 10 games that were remaining, it was always going to be difficult to win all 10 of them.
"So we'd built (factored) in a loss and maybe some draws in that
We hoped it wouldn't be in this game against a rival, but it's still very much possible.
"There's five points between us and them
We've now got to recover and use this as the same springboard we did in the last game.
"We'll go away now and recover and look to get a victory in our next game (away to Arsenal), which we've shown we're more than capable of."
Source : AFP