Parkinson has been in charge of the club since April 2016, and in his first three years at the helm, Town secured two promotions.
Daventry are currently second-bottom of the Pitching In NPL Midlands Division, and the club say his departure is partly due to financial constraints.
A statement read: “To climb back up with such limited resources is testament to Parky being able to attract players to Daventry Town Football Club.
“The journey with Parky has been a joyful one, and one of his best attributes has been the togetherness of the teams he has assembled over the years.
“This season has been tough, with so many close results going against us. Without a major sponsor next season in Step 4, it would see the club again looking at relegation from the start.”
On his departure, Parkinson said: “It is with deep regret that today I have resigned as manager of Daventry Town FC.
“After discussions today with the board regarding the finances of the club, it seems the right time for me to step away.
“The club at this minute in time doesn’t have the resources to play Step 4 football and, because of this, it was a fairly straightforward decision for me to make.
“The club’s future is far more important than my own personal ambitions and I fully understand and respect their decision, although I’m also disappointed as I felt we would have survived relegation.”
The club have not confirmed whether a successor will be in place ahead of next Saturday’s trip to league leaders Halesowen Town.
Photo credit: Daventry Town
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