Salah recovered from a first-half penalty miss to score twice and add another as Jurgen Klopp’s side won a New Year’s Eve thriller 4-2 at Anfield to move three points clear at the top.
It was his last game before joining Egypt ahead of the upcoming Africa Cup of Nations.
Salah told Sky Sports: “It’s a great result for us. The game was very heated and we managed to get three points and now we are at the top of the table. We have to stay calm and win every game.”
Asked about his team’s chances for the title, he added: “We believe a lot. We have to work hard and express ourselves on the field. If we can do it and work hard, we can keep winning.”
Salah was delighted not to retire from club duties quietly after seeing his free-kick – the first of two he had during the match – beat Newcastle’s impressive goalkeeper Martin Dúbravka.
He said: “I miss the pen – I didn’t want to leave with the national team with this performance.
“The first one I was confused because the goalkeeper moved, but I did the second one like in training.
Salah opened the scoring with a tap-in early in the second half. The effort was quickly canceled out by Alexander Isak but Liverpool took control through Curtis Jones and Cody Gakpo.
Sven Botman pulled off another save but Salah wrapped up the win for the home side – who had 34 shots – deserved after Dúbravka’s foul on Diogo Jota.
Liverpool manager Jurgen Klopp said: “No one should really be surprised that Mo can change the game. The more goals you have, the more you’re used to missing chances and you understand what you need to do to keep going and improve, and that’s what Mo did.
“It was a super match from start to finish, super high intensity. I loved so many aspects of the game apart from conceding goals.
“It was an incredible match with an incredible atmosphere.
Newcastle boss Eddie Howe admitted his side were lucky to go clean at half-time but struggled with both free-kicks against them.
“I’m still confused by the penalties we gave away. Especially the second one didn’t look like a penalty,” he said.
“There are two ways to look at it: the challenge on Sean Longstaff (in the second half) was a pen for me and it changed the game massively and then they went down the other end and it wasn’t (a penalty). ”
A fifth defeat in six league games and one win in 12 away games has left Newcastle struggling to stay within reach of the top four.
“We have to do everything we can to protect that trust, so I think we don’t need to over-dramatize things,” Howe added.
“It was a really good performance from Liverpool, they made it very difficult for us – we did well to go 0-0.
“Take away the penalty moments, the goals conceded were disappointing.