Quickfire second-half goals from Willy Gnonto and Ao Tanaka turned the tie in Leeds’ favour after they had trailed at half-time to Beb Brereton Diaz’s opener for Derby.

Brereton Diaz struck against the run of play soon after Leeds striker Joel Piroe had seen his penalty saved, while substitute James Justin rubberstamped the visitors’ progression with his first goal for the club in added time.

Farke said: “I’m a big believer in cup competitions. I know some people see them as a distraction from the league, but I love cup competitions.

“We want to try to come as far as possible in the FA Cup, otherwise we would have sent a different team out today. We wanted to travel with the strongest possible squad without taking any risks.”

Farke made eight changes after his side’s cruel 4-3 defeat at Newcastle four days earlier, but only briefly did Leeds look like succumbing to an upset.

“Of course we’re not the favourites to win this competition. We know this,” Farke added. “But if cup competitions are made for fairy tales, and if there is a chance, then we want to be involved.

“I want to stay humble. I don’t want to speak about Wembley right now, but it would be great to write another chapter of big history for this amazing club.”

Derby boss John Eustace, who handed debuts to Danish midfielder Oscar Fraulo and teenager Owen Eames, had no complaints after making six changes following last week’s home defeat to Wrexham.

Eustace said: “I thought we were really good value for money and we got some vital minutes into so many players that needed it today.

“We were really competitive and I was pleased with the effort. I just wanted the team to be competitive today. I wanted us to win, of course I did.

“But the bigger picture is that there’s five or six players who desperately need minutes under their belt because they haven’t played at all for much of the season.”

Eustace has backed Leeds, who sit 16th in the Premier League, eight points clear of the bottom three, to maintain their climb away from relegation trouble.

He added: “I think there’s a good chance. There’s already a big points margin.

“Obviously Daniel’s adapted to the Premier League and changed his style a little bit. It’s great management and they’ve been picking up points now.

“They’ve got an awesome squad and a very good manager. So yes, I’m sure they will do.”