Heung-Min Son’s second-half effort condemned the Citizens - who missed the chance to take an early lead via Sergio Aguero - to a 1-0 defeat at Spurs’ new stadium.
Manchester City will hope to get the required result to move to the competition’s semis for the second time ever when Mauricio Pochettino’s side come visiting the Etihad next Wednesday.
"At home, we are very good," Mahrez said, per Manchester Evening. "We're going to give everything and I feel we can win.
"We will never put our heads down. It was a difficult game. Even if we drew we still have to win our game at home so it doesn't change our approach.
"Of course, it was a difficult game. We know Tottenham, a physical team, a lot of intensity. It was the game we expected."