Salah was the team's best performer in January, and has been recognised by fans as such.
The Egyptian played seven games for the Reds in January, scoring five goals.
He told the club's website: "Thank you. Of course I'm happy to win this award but I'm always saying that every time the team comes first.
"It's good to win trophies individually but we just need to focus in that period and try to win games and go through the right way.
"I think last month was better than months before but we still need to win games. When I score goals and help the team to win games, that's what makes me happy.
"But if you score goals and the team is still not winning, that's not a great feeling. So we just need to carry on and I'm trying always to score goals to help the team.
"I think they [the fans] always support us, especially when they were in Anfield. But now with COVID they cannot come but I'm sure they're always supporting us.
"We just need to stick together and carry on, win games and stay with each other."