The 22-year-old full-back netted the opener in the 34th minute when he cut in from the left, going past Tommy Smith and Joe Allen in the process, and sent a superb shot into the top corner from just outside the box.
Asked where it ranked in the list of his goals, Justin told LCFC TV: "It's number one to be fair, it's number one. I haven't hit one better than that."
The England Under-21 international added: "I just looked at him and then cut in on my stronger side, saw another man coming, pushed it out, and I thought why not?
"If you don't shoot, you don't score, it ended up in the back of the net, and I'm delighted with the goal."
The Premier League side doubled their lead in the third-round tie through a cool Marc Albrighton finish just before the hour mark.
Ayoze Perez subsequently struck number three for Brendan Rodgers' men in the 79th minute, and Harvey Barnes then added a fourth two minutes later as he lashed the ball past Joe Bursik.
It was a ninth goal of the season and third in four games for Barnes, who had twice been thwarted by Bursik in the first half.
The England winger said: "When I've been in good form, you get a bit of confidence, and I think in front of goal, I feel really confident that I'm going to get the ball and have chances in the game.
"At the minute, they're going in and I'm really happy with that.
"There were times in the game where we played really well, and we scored some great goals."
Jamie Vardy and James Maddison, both of whom had been nursing injuries, were missing from the Leicester line-up.
Their replacements, Perez and Dennis Praet, were the only changes made by Rodgers from the win at Newcastle a week earlier, with the Foxes not in action again until next Saturday, against Southampton.
When asked about the strength of the Foxes team, Stoke boss Michael O'Neill – who made five alterations to his XI – said: "I didn't expect Brendan to come and play anything other than that. Even without Maddison and Vardy, they still had quality.
"For some of our players, it gave them an indication, particularly some of the younger ones, of the level that's required to play at the top end of the Premier League. Once we went behind it was going to be very difficult against that level of quality."
Stoke are currently eighth in the Championship, and O'Neill added: "I don't think that will affect their confidence really in terms of the Championship. We recognise the quality we played against.
"The most important thing is we now know we have 23 league games left, and we can make a real fight to finish in the top six."