Nelson came off the bench on Sunday, following an injury to Bukayo Saka, and scored twice as Arsenal ran out 5-0 winners to go back to the top of the Premier League.
It was the first time since July 2020 that the 22-year-old had scored in the Premier League, having spent last season on loan at Feyenoord.
Nelson returned to Arsenal this summer and is determined to make his mark with any chances he gets.
“It was amazing - like I was playing FIFA a bit, you know,” Nelson said of his performance. “I think the first one - Gabi (Jesus) saw me in the box and I knew I could get there, so I had to get there.
“I was going to take it first time, and I kind of rolled it onto my left and hit it, and then I think the keeper saved - and I was gutted. Then it came back out and my eyes lit up and I just hit it ... and it went bang into the top corner. So I was really delighted.
“Then the second one, I was just busting my gut to get into the box, and I think I got there and, of course, I just placed it into the corner. But like I said, I’m just really happy, and just overwhelmed by the occasion.”
Having made his Arsenal debut in 2017, Nelson saw the likes of Saka and Emile Smith Rowe come through the academy and overtake him in the pecking order.
“I’ve been waiting patiently,” added Nelson. “I’ve been on loan, and sometimes you feel like it’s not going to come. But of course, I believe in God, and I believe in myself, and I believe in the team. So I’ve just been patient and ready for that. Ready for the opportunity to come.
“I think it gives me all the confidence in the world and like I said I’m just going to keep training every day, like I can. Hard as I can, if I get another opportunity just to keep going, helping the team really - and just keep pushing on.”