The Colombian winger has joined the Bundesliga champions in a £65.5 million move from Liverpool and is determined to prove himself in Bavaria after scoring on his competitive debut in the 2-1 win over Stuttgart in the German Supercup at the weekend.
Diaz told ESPN: "I'm very happy and pleased with how this weekend went.
"As you pointed out, it was my first official match, my first goal, and my first title. I dreamed of coming here to achieve great things and give my best. I try to enjoy football.
"It was a big gamble and I'm very grateful to the management for reaching out to me and trusting me. It's always up to me to respond on the pitch and contribute with what I know how to do. To be at the disposal of the coaching staff. To start this way and be together with my team-mates is incredible."
Diaz revealed that he spoke to Liverpool's Florian Wirtz - who moved to Anfield from Bayer Leverkusen this summer - to get an idea of what he can expect in the Bundesliga.
He said: "I already had some knowledge of the Bundesliga. I love watching football and all the competitions. I had the opportunity to talk to Florian in Liverpool, and I know it's a physical league. I hope to have a great debut. I've been here at the club for about two weeks, and I need time to settle in."
Diaz paid tribute to his former Liverpool team-mate Diogo Jota, who tragically died in a car accident alongside his brother Andre Silva last month, with his goal celebration and says the unexpected loss of Jota has been "brutal".
He said: "It's brutal. The fact that he's no longer with us and that we've lost an incredible teammate is unbelievable. No one is prepared to receive this kind of news and feel OK when faced with a situation like this.
"He was a great teammate to me. We will remember him fondly. He will live on in our memories, and being able to dedicate the goal to him is something special. I had planned to do so."