Chiesa came on in the second-half in victory over Bournemouth.
Asked if the atmosphere met his expectations, he told Liverpoolfc.com: “Yes, yes, yes, it did! Hearing You’ll Never Walk Alone for the first time from the bench, it was amazing.
“It was amazing also against Nottingham Forest, but unfortunately we lost, but today was really amazing. I enjoyed every bit of it.
“I think I played seven minutes in Milan, I played not too much, but I was very, very happy to make my debut in Milan and today I just had to be ready and when the coach told me to get in the game I was so happy and so relieved because I wanted to play here at Anfield.
"Yeah, it was a big result for us. I think we showed a great performance today after a big loss against Nottingham Forest at home and today we wanted to show that we are a big team, a great team that wants to perform at the highest of levels."