Brechin lost 3-0 on aggregate to Cowdenbeath in the play-offs.
"I felt if I made the decision now, it would let Brechin get a new manager in, which is important for their future," Duffy told BBC Scotland.
Duffy was director of football with Hearts in 2006 and had coaching spells with Chelsea, Portsmouth and Norwich, but insisted he had parted on amicable terms and was not seeking an immediate return to coaching.
I felt it was the right time for myself to try and move on. I don't have anything up my sleeve, but I just felt I had given the part-time situation a go for a couple of seasons and it was a great education for me
Jim Duffy
"It's something I've thought about for the last couple of months," said Duffy.
"I just wanted to get to the end of the season and give everything we had to try and achieve promotion.
"Unfortunately, we fell at the final hurdle.
"I felt it was the right time for myself to try and move on. I don't have anything up my sleeve, but I just felt I had given the part-time situation a go for a couple of seasons and it was a great education for me.
"The club were terrific and the chairman was excellent. I have a good relationship with everyone at the club."
Duffy insisted he would be interested in taking on a more permanent, full-time role at some point in the future, but denied he was interested in the vacant managerial position at Morton or in a return to manage in the Scottish Premier League.
"I haven't applied for any jobs or used contacts to apply for any jobs," said Duffy.
"I've just left Brechin and I have some family issues to deal with over the coming days and months.
"Once those are finished, hopefully, there will be a brighter time around the corner."
Source: BBC Sport
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