Pep Guardiola's side fell to a 1-0 defeat at the Tottenham Hotspur Stadium in the first leg of our quarter-final tie with Tottenham on Tuesday.
Heung-Min Son scored the only goal of the game in what was a tight battle throughout.
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Despite the narrow defeat, the Algerian believes City hold the advantage by returning to the Etihad Stadium - where we have won 23 of 25 matches this season - for the second leg.
"At home we are very good," he said. "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."
Tuesday's game was a closely contested game, with very little between the two sides.
And speaking immediately after the full-time whistle, Mahrez said Spurs' approach was the one City expected.
"Of course, it was a difficult game," he said. "We know Tottenham, a physical team, a lot of intensity. It was the game we expected."
City host Mauricio Pochettino's side for the second leg of our Champions League quarter-final tie at the Etihad Stadium on Wednesday 17 April, with kick-off at 8pm BST.