Derby had a 1-0 lead at halftime before Leeds fought back after the break to win 3-1 through goals from Wilf Gnonto, Ao Tanaka and Justin.
The defender said afterwards: "We knew coming into the game it was going to be a difficult one.
"We had to weather the storm, I'd say, in the first 15 or 20 because they were at it and after that, I feel like we took control of the game.
"It's a great feeling to be in the next round and to be honest, with the traveling crowd here, it felt felt like we're at home and just the support was top as always. We hopefully never let them down.
"In football, things can go either way, and it's just about the heart and spirit you show on the pitch and the performances and then the results will come in the end."
On his first goal for Leeds: "It was a great feeling at the end of the game. I think I got a rush of blood when I got in front of the goal. Luckily, it went in the back of the net and it was a nice little cherry on top."