Jurgen Klopp's side ran riot in the 202nd meeting of English football's biggest rivals.
Naby Keita and Diogo Jota put Liverpool two goals ahead early on before Salah turned on the style with his treble.
United played most of the second half with 10 men after Paul Pogba was sent off in a chastening afternoon for Ole Gunnar Solskjaer's team.
It was Liverpool's biggest ever win at Old Trafford and their largest success against their old foes at any venue since 1925.
"I think it is great to win 5-0 here, we knew before the game it would be tough if we did not play our game," Salah said.
"We knew they will come and try to give everything so we had to give 100 percent. We just tried to play our football and play in between the lines to create more chances. We did that and were lucky to score.
"As long as the team keep winning I am happy and to give my best to the team to win. The first goal I gave to Naby Keita to score."
Salah is the first away player to score a treble at Old Trafford since Brazil legend Ronaldo in 2003.
He also surpassed Didier Drogba to become Africa's all-time leading scorer in the Premier League with 106 goals.
The 29-year-old has now scored in 10 successive games in all competitions, while Liverpool are unbeaten in their last 22 games in all competitions.
Liverpool are second, just one point behind leaders Chelsea, and look poised for a sustained assault on the English title currently held by Manchester City.
"We know what it takes to win the Premier League, we did it two years ago. A big win here but still only three points," Salah said.
"We try to win each game and try to win the title. We need to play to win everything. From our heads from pre-season, we need to win the Premier League and hopefully we go for that.
"After half-time we were talking in the dressing room to just keep going and score as many as we could."
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