Rodgers shocked supporters of the Scottish champions on Tuesday by departing after winning all seven domestic trophies on offer during his near three-season reign in Glasgow.
"It was a very, very difficult decision. If I was making this decision with my heart then I'd be at Celtic for life," said the Northern Irishman on Friday.
"I was presented an opportunity that came to me and then of course, emotionally, you have to take that out."
Rodgers said his decision had even left some of his family upset and Celtic fans responded by hoisting a banner at Wednesday's 2-1 win over Hearts that read: "You traded immortality for mediocrity: never a Celt, always a fraud."
However, the former Liverpool manager claimed he could not resist the lure of the Premier League.
"Celtic is one of the biggest clubs in world football, you can't deny that. It's one of the reasons I went to Celtic, it's a huge club in every single way," added Rodgers.
"There is an intensity, demand and expectation to play at Celtic not matched by many teams in the world, but for me it was about the challenge and coming to the Premier League with a club with the ambition to keep moving forward and progressing."
Leicester are currently 11th in the table and out of the FA Cup, but Rodgers believes European qualification and winning a trophy are his objectives.
"The expectancy is to challenge for a European place and look to win a trophy. That has to be the expectation," he added.