The Foxes won the competition for the first time in their history last season; beating Chelsea 1-0 in the final at Wembley but became the second Premier League side after Arsenal to be eliminated by Forest this season.
Leicester were down 3-0 after 32 minutes and even though Kelechi Iheanacho pulled one back five minutes before halftime, it could not inspire a fight back and they conceded a fourth on 61 minutes.
Rodgers apologised to the Leicester fans for the poor display and has charged his boys to improve.
"It was an awful performance and I have to apologise to the supporters,” Rodgers said.
“To come here, the first game between the two sides for a long time, a great atmosphere, in derby games you need authority and you need physicality. Those two were sadly missing from our performance.
"I said to the players after that for the first time since I’ve been here I’ve been embarrassed. It was an embarrassing performance. I feel for the supporters and the excitement of coming here.
“We brought the FA Cup into our team meeting today so the players could see what we went through last year to win this competition, to remind them of the day at Wembley and the journey, and what it takes to win a trophy like that.
“I was looking to provide that motivation and extra desire to come out here today.
