The Algeria forward completed a club-record £60million switch to the Etihad Stadium earlier this week.
City set a host of records as they powered to Premier League title glory last season and transferring that success to the European stage is now one of the club’s next aims.
Speaking at his formal unveiling at the City Football Academy, Mahrez said: “It’s a club who wants to win this type of trophy. The Champions League is for big clubs and Manchester City are a big club.
“They have everything to try to win the Champions League. It is a goal. Last season they lost in the quarter-final and I know they have the ambition to go further the next season.
“That’s why I’m here, why I made the decision to come here, because I want to be part of this.”
Mahrez, 27, temporarily stopped training with Leicester after a move from the Foxes to City failed to materialise in January.
City had enquired about the 2016 PFA player of year in the closing days of the transfer window but refused to meet Leicester’s asking price.
Mahrez was keen to steer discussion away from that issue as he took questions from media.
He said: “They (City) offered and Leicester rejected the offers, but it’s the past. Now I’m here now and I’m happy. This is the past and we are looking forward now.
“The most important thing is I’m here. I’m starting a new challenge and a new life. It’s a good thing.”
Mahrez did thank City for reigniting their interest in him this summer.
He said: “That means a lot for me. I’m very happy and will give my best to this club.”
The final fee represents a considerable reduction on the £95million Leicester were reportedly asking for in January but it is still a sizeable outlay, eclipsing the £57million City paid for Aymeric Laporte last season.
Mahrez said: “The prices have been very big in every country so it doesn’t affect me.”
Mahrez has been in demand since Leicester’s run to Premier League glory in 2015-16 but he hopes the move has come at the right time in his career.
Asked if he should have left the King Power Stadium sooner, he said: “Maybe, but it is the destiny. It happened like this. If I’d moved sooner maybe I wouldn’t have been happy, I don’t know.”
Mahrez is now looking forward to working with manager Pep Guardiola and the rest of the squad, who won the title with a record 100 points and 106 goals.
He said: “He’s a big manager, he’s won a lot of things, made history with this club. I wanted to work under him and to play in this club. I didn’t hesitate at all.
“What they did was amazing work. They broke all the records in the Premier League, which is unbelievable. I’m very confident about myself and I hope to help this team to improve.”
Mahrez is City’s first signing of the summer and has signed a five-year deal.
The 27-year-old participated in basic training drills along with the rest of the squad and showed plenty of flicks and tricks.
The 27-year-old Algeria winger joined Premier League champions City on Tuesday for what was described as a “club-record” fee reported to be in the region of £60million.
“To all Leicester fans, we have made some amazing memories and history together,” Mahrez said on his personal Twitter account.
“Winning the Premiership (in 2015/16) against all odds was just something else and none of this would have been possible without your extraordinary support for me and the team.
“I want to thank all of you for welcoming me to the club right from the start and continuing to give me the belief and encouragement to achieve what we have together.
— Manchester City (@ManCity) July 10, 2018
“I would also like to thank my teammates, staff and everyone at the club who have become a big part of my life in the last few years.”
Mahrez was wanted by City boss Pep Guardiola in January when Leicester rejected their £50m offer plus winger Patrick Roberts, who was valued at £15m.
“Now it’s time for me to move on and try to build on what I have developed here, but I will always remember my time at the club with great joy and pride,” Mahrez added.
“Thank you, Thank you, Thank you.”
Mahrez – who missed two Leicester games after his proposed January transfer collapsed – was given extra time off by the Foxes after playing in Algeria’s international games in June.
He had been set to return to pre-season training before confirmation the protracted transfer had finally been concluded.
To all Leicester fans,
We have made some amazing memories and history together. Winning the premiership against all odds was just something else and none of this would have been possible without your extraordinary support for me and the team. I want to thank all of you
— Riyad Mahrez (@Mahrez22) July 11, 2018
Provided by Press Association Sport