Shock 2015-16 Premier League winners City also have a Champions League last-16 tie with Sevilla on the horizon.
Rams assistant boss Powell told BBC Radio Derby: "The season they had was quite unique, it won't happen again.
"They're now having their Champions League excursion and that's something we aspire to."
Powell, who reached the quarter-finals of the FA Cup as a Derby player in 1997, ended his career with Leicester in 2010, before briefly being part of the Foxes' coaching staff.
He is excited by the prospect of facing the Foxes on Friday and said their current struggles, coupled with Derby's home advantage and impressive form in the Championship, made the televised tie a tight one.
The Rams have lost just three of their matches since Steve McClaren became boss in October, while Leicester have lost 11 of their 22 Premier League matches this season.
"It's going to be some game," Powell added. "People may say Leicester are the favourites. But with home advantage, and what Leicester are going through, it's an opportunity for us to take advantage."
After stints in charge of Charlton and Huddersfield, Powell returned to Derby in May as number two to Nigel Pearson and retained that role when McClaren took over.
Having been a player, coach and caretaker-manager of both East Midlands rivals, Powell said he could see parallels between the clubs.
"For passion, and for supporting your team, they are very similar," he said prior to the fourth-round tie at Pride Park. "Up until quite recently, their history was kind of similar as well.
"But of course Leicester have surpassed what most clubs, apart from the traditionally big clubs, have done."
Chris Powell hopes Derby County can emulate his ex-club Leicester City's achievements as the East Midlands duo prepare for Friday's FA Cup meeting.