Jurgen Klopp's side claimed a 2-1 win over the Premier League leaders at the Etihad Stadium on Tuesday and a 5-1 aggregate triumph in their quarter-final tie.
Trailing 3-0 from the first leg, City threatened a famous comeback when Gabriel Jesus scored after just two minutes, and Liverpool survived sustained pressure and a contentious offside call against Leroy Sane to ensure they were only a goal down at half-time.
The visitors responded in style after the break, though, with Salah's 39th goal of the season and a strike from Roberto Firmino securing their last-four spot, after Pep Guardiola had been sent to the stands for confronting referee Antonio Mateu Lahoz at the break.
Salah has now been involved in 50 goals in a remarkable first season with Liverpool, but he insists results are all that matters.
"They were pressing very high and had many chances but we came back and played hard and the win was deserved," he told BT Sport.
"I try to play for the team and try and score in each game and that's the most important thing for me."
James Milner was proud of the way his team-mates coped with City's first-half pressure, but admitted they have room to improve ahead of the semi-finals.
"They're a good team and they were always going to put us under pressure," said the former City midfielder. "They had chances but that shows a lot about how we came out in the second half.
"Maybe it woke us up to concede that early, it says a lot about the boys coming under that pressure in the first half and in the second half last week. In the second half today, we got hold of it slightly more, but we still have to improve.
"Everyone knows how good Manchester City are, so to beat them is a good confidence builder but we have to be better in the next round.
"We got about them a bit more in the second half, kept the ball slightly better, were more composed. That's the key, it's what you have to do against these sorts of teams."