The Brazil striker hit a brace on Tuesday as the Gunners won this Champions League tie 3-1.
He remarked afterwards: "It's a dream night. I always dreamed of being a footballer.
"I watched a lot of Serie A when I was a kid, so to be here in this stadium and score here (produces) tears in my eyes, because I always dreamed of being here.
"There is always a reason why things happen, whether it's good things or difficult things. I learned that during my 11 months (injured).
"It is always difficult to play against Inter Milan. We came here last season and lost (1-0 during the league phase). Tonight we played better than them and controlled them, but they are a top team and they attack.
"We scored at the end and got the three points. We have to keep going."
On competition for places at Arsenal, Gabriel Jesus added: "Everyone wants to start. I am a very respectful guy. I am not a kid anymore – I am 28, so I understand football. I am very happy Vik (Gyökeres) came on and scored.
"I am so happy I scored and Vik scored. I am confident Kai (Havertz, who is returning from injury) will score when he gets the chance."