Altrincham manager Ken McKenna and assistant Stuart Bimson have decided to leave Moss Lane after the club's relegation to Blue Square Bet North.
The Robins were relegated after a 4-3 home defeat by Eastbourne on 30 April.
McKenna said: "It was a very tough decision, but perhaps it is best that someone new comes in with their own people and own ideas."
He also cited prospective cuts to his backroom staff as a reason for leaving, but praised chairman Grahame Rowley.
"There are some outstanding people at the club who put so much into making it work," McKenna continued. "I've got nothing but praise for the chairman.
"Grahame backed me 100% at all times and even allowed me to go well over budget in an attempt to stay up.
"He was really flexible - no manager can ask for more than that - and it made it all the harder for me to walk away."
Former Robins player McKenna, who took over the manager's post after Graham Heathcote's exit on 14 September 2010, broke broke the news to Rowley on Sunday.
The 50-year-old succeeded Heathcote with the club bottom of the Blue Square Bet Premier, taking just one point from their opening eight games.
Results steadily improved under McKenna and a win against Eastbourne would have secured the Robins' safety. But after coming from three goals down to level the game, they were beaten by George Purcell's last-minute goal.
"I'm still shellshocked at what happened on that final day," McKenna added. "I just need to step back, gather my thoughts and consider what to do next.
"I would urge anyone interested in succeeding me to go for it, because it is a fantastic club with a very loyal support.
"Whatever happens, I won't forget my time at Altrincham - I loved every minute. I wish everyone there all the very best and, as has been the case for the past 20 years, I will be looking for their results."
Chairman Rowley said: "'Ken had been giving his position plenty of thought, and I was sad to hear his decision when we met up. But we parted on very good terms, and I have nothing but admiration for him.
"He took the job on in very difficult circumstances, but if you took his points per game average since then and extended it over the season, we would be mid-table.
"It was a superb effort, and I always found him a very honest chap to deal with. We had some very honest conversations, even at the end of the season, and I haven't a bad word for him."
Altrincham immediately began their search for a replacement.
"This is a fantastic opportunity for someone to take charge of a great club and steer the ship back in the right direction," continued Rowley.
"We are looking for someone who has knowledge and experience of Blue Square Bet North, because it is quite different from the Premier.
"There are no parameters regarding experience in general. It could be a manager who has been around a while or someone up and coming."
McKenna scored 56 goals in 100 games in a two-year spell as a player at the club from 1990-1992 before re-joining the Robins in July 2009 as assistant manager.
He was formerly manager at Welsh club The New Saints, where he won a hat-trick of Welsh Premier titles.
A statement on the club's website thanked both McKenna and Bimson for "their efforts and commitment".