Mahrez made only his 14th start for City in Sunday's 4-1 win over Brighton, in which he scored a brilliant goal.
Despite the competition for places, the Algerian has no doubts whether he is good enough to play at the Etihad.
"It is not easy to come to a team who are settled, who have players who play," said Mahrez. "That squad did everything last season.
"I knew it would not be easy in my first year but I am very confident in myself and have no doubts about my quality. I knew that when I had my chance I would take it. I scored at Brighton and helped the team.
"I am very happy here. I am not going somewhere else because I don't play. It's part of the game. I need to be strong, stay strong. It's part of my personality, I never hide away from things."