Jürgen Klopp's team needed to show plenty of patience to claim three points from a sturdy opponent in Rafael Benitez' Magpies. Newcastle were well organised and looked to frustrate Liverpool to plenty of chances in a cagey first-half.
The deadlock was broken on the 40th minute when Mohamed Salah was slid in by Alex Oxlade-Chamberlain to fire his 32nd goal of the season.
Mane added to the hosts' tally early in the second-half to ultimately give the Reds some breathing space, but the Senegal international insists it was anything but for the players.
He told Liverpoolfc.com: "I'm very happy. It was not an easy game but, like always, we tried and tried again and in the end, we got three points.
"I think we deserved to win this game today, even if it was not easy because Newcastle is a very well-organised team.
"They didn't give any space in the beginning but we just [kept trying].
"After we scored the first goal it was a little bit easier for us because they tried to open the game", Mane added.
"It was not easy but this kind of game can happen. As a team, we were solid and did what was important to win the game.
"You can't play every game 100 per cent but hopefully the next game we will be."
Back four and goalkeeper did 'great job' to ensure the win
Liverpool's victory over the Magpies also secured them their fourth clean sheet in six games as they kept quite a well organised Rafael Benitez side at Anfield.
Mane also was full of praise upon his back four and goalkeeper Loris Karius for the part they played in providing a platform for victory.
Karius saved spectacularly from Mo Diame after Newcastle worked a chance in the Liverpool box. The ball rolled out to Diame on the edge of the box and his effort - arrowing certainly for the top right-hand corner - was pushed away by the German keeper.
Mane added: "All the time it's very important because sometimes it's difficult, you can't score a goal.
"If you get a clean sheet it helps because, if they score against you, you have to get two more goals to get the three points.
"But they did a great job behind us and they pushed us."