The 19-year-old midfielder netted a pair of opportunistic finishes before half-time to put the Gunners in control of an entertaining tie, and giving him the second and third goals of his senior team career.
He thought he had a third 10 minutes from time but the goal was ruled out due to offside against Sead Kolasinac.
It proved inconsequential to the scoreline with Alex Iwobi netting a third to give Arsenal a 3-0 victory over the League One club.
And while Willock, who has yet to make a Premier League appearance this season, was saddened he was narrowly denied the hat-trick, he hopes the performance will force Unai Emery to give him more chances.
"It's a brilliant day for me on a personal note but I'm proud of how we did as a team as well. I don't think the scoreline reflects how well we played," Willock told BBC Match of the Day.
"I always try to get in the box and make myself available for crosses or rebounds, so it was good to get two goals.
"The linesman crushed my dreams with the hat-trick but that's football and hopefully I can get another opportunity soon.
"Hopefully the boss keeps believing in me and giving me opportunities. I'm always eager to play, so I'll always do my best if I'm picked."
Speaking to BT Sport, Iwobi reserved praise for his young colleague.
"It's good we have the youngsters who can come in and perform like Joe," he said.
"It's a good headache for the manager if everyone who plays does well."
Arsenal are next in action next Saturday in a London derby away against West Ham.