Mahrez said: "At the end they pushed but we handled the situation very well. We go back with the three points.
"We knew once we scored the first it opens up the game, we had more space. We had chances to kill the game and we didn't."
City captain Vincent Kompany added: "It was a good old Premier League game, as soon as they scored long balls start coming, they are extremely physical up front. Credit to us for staying strong.
"I don't think we ever lose focus. We had chances to make it 3-0 and anytihing can happen. We managed the game pretty well. You can't win every game playing fantasy football."