Hugill was on target in Tuesday's 2-2 draw with Bournemouth, with the Cherries then winning 5-3 on penalties.
He has not started a league game for Norwich since the end of the 2020-21 season, spending last term on loan at West Brom and Cardiff City.
"I've had to be patient," the 30-year-old told BBC Radio Norfolk.
"From the start of pre-season, I've scored goals when I've been on the pitch.
"Another goal tonight hopefully strengthens my case but we'll see what happens and just carry on."
Hugill joined the Canaries from West Ham two years ago in a deal that could eventually be worth £5m.
He scored five times in 34 appearances in 2020-21 as they won promotion to the Premier League, but remained in the second tier as he was sent out on loan.
"There's a good, healthy competition [for places]," said Hugill.
"The relationships between everyone at this club are fantastic - we've got a tight squad and the younger lads that have come in have fitted in perfectly.
"When I'm not playing, I want everybody else to do well - we're just pushing each other to be better."
He added: "Ultimately, you want to play, especially with the pre-season I've had, I've scored seven goals now, but I've got to wait for my chance and when they come, I've got to be ready to take them."
Norwich led Bournemouth 2-1 in the second round tie, only to concede an equaliser in stoppage time.
"If we'd gone through, I'd have said we'd been fortunate," said boss Dean Smith.
"They created the bigger chances in the game - Angus [Gunn] made two outstanding saves for us.
"When you get to that 92nd minute, you've got to do the basics right, you've got to stop the cross and defend the box and we didn't do that, we let them off the hook at the end."