Salah added his third moments into the second half before Paul Pogba was sent off for a dangerous tackle.
"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 after the game.
"We knew they will come and try to give everything, so we had to give 100%.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."
Bruno Fernandes had an opportunity to open the scoring for United after just four minutes but blasted over the crossbar.
Liverpool responded to the scare with a goal on five minutes after poor defending from United saw Luke Shaw attempting to mark Salah, Keita and Andy Robertson. Salah chose to play in Keita, who hit the ball past David de Gea.
United were guilty of more poor defending on 13 minutes, when Trent Alexander-Arnold put a low cross into the box and Jota stretched to place it in the net.
Salah scored his first goal on 38 minutes with a low sidefoot past De Gea and his second five minutes into added time at the end of the first half with a superb strike from the corner of the box.
The Egypt international completed his hat trick five minutes into the second half. His three goals on Sunday make him the top-scoring African player in Premier League history, overtaking former Chelsea forward Didier Drogba by two goals.
"I am so disappointed, we gave them so many chances," United captain Harry Maguire said. "They were so clinical, we had a lot of chances ourselves, but I am a defender and to concede four in the first half, especially at Old Trafford, is nowhere near good enough
"As a player I know myself. I'll be looking at myself and my individual performance.
"We have to stick together, there is no point blaming each other, but look at ourselves. Look in the mirror when we go home tonight and think where we can do better.
Cristiano Ronaldo thought he had pulled one back for United on 52 minutes with an excellent piece of individual skill, but VAR replays showed he had been offside in the build-up, and the goal was disallowed.
United's day went from bad to worse when Pogba was sent off on the hour mark for a studs-up challenge on Keita, who had to be stretchered off the pitch.
Liverpool manager Jurgen Klopp said he did not expect a 5-0 result.
"Pressing high, winning balls, scored wonderful goals," Klopp said. "I told them at halftime to play better. We started incredibly well and stopped playing football. We controlled the game after the fifth, it was not about scoring more, just trying to get out without more injuries.
"The result is insane, I asked if there was one like this in history and if there isn't, then it will take a while. The players put a nice piece in the book. It is special, but we don't celebrate like crazy, we have respect for the opponents. We were lucky in some moments; United are not in their best moment."