It was the Egyptian’s 21st strike in the tournament’s main phase, excluding qualifiers, for the Reds and matched the tally achieved by Gerrard.
Collecting Curtis Jones’ clearance from a corner, Salah carried the ball the length of the opposition half on 47 minutes before curling a finish beyond the goalkeeper.
“Of course I’m very happy to be the highest one. Steven Gerrard is a legend for the club. It’s something I’m very proud of,” he said post-match.
“But as I’ve said before, the most important thing is the team. So I’m happy to score goals to help the team to win games, that’s the most important thing.”
Liverpool lead Group D by five points having won each of their opening three games in the section without conceding a goal, and can qualify for the last 16 if they beat Atalanta when the sides meet on November 25.
Atalanta 0-5 Liverpool: Watch highlights via LFCTV GO
Summer signing Diogo Jota continued his sensational scoring form with a hat-trick at Gewiss Stadium and Sadio Mane was also on the scoresheet in an emphatic display against a team who reached the quarter-finals last season.
Asked about the Reds’ prospects of lifting the European Cup again, Salah said: “It’s tough, I don’t want to put pressure on us.
“But I think we are doing good in the Premier League, we’re doing good in the Champions League. As Liverpool, as a team we have to fight for everything – that’s our job, that’s why we have to put pressure on ourselves.
“I’m sure we’re going to fight in each competition, in the Premier League as well. We want to win everything and hopefully we can do it.”