Vale needed a win against Fleetwood Town on the final day of the season to keep their place in the third tier, but they could only manage a goalless draw as their four-year stay in the division came to an end.
Smurthwaite became chairman of the club in 2013 after being part of the investment group that took them out of administration the previous year, but he has now admitted to "seriously damaging" the club and vowed not to attend another match at Vale Park.
"Valiants, I took up the chairmanship of this great club four years ago, with the football club and its parent insolvent, a very large unpaid creditors list, and with no knowledge whatsoever of running a football club. Admittedly I seriously considered putting the club back into administration but the consequences of that would have been catastrophic so, having made my peace with Micky Adams, we agreed a course of rebuilding our club," read a statement from the 54-year-old on the club's official website.
"I did not realise what a big asset Micky Adams was until he left us who, in reality, he was much more than just the manager. On his departure I became vulnerable without his structured management of the football department. Being focused in trying to stabilise the club I ignored and took for granted the most important asset the football club has, and that is you the supporters. When I really understood that, I think for some of you that was unfortunately too late.
"In thinking outside the box last summer I have clearly seriously damaged our club, resulting in Sunday's relegation which was never my intention as the club is now a very big part of my life. I deeply regret the actions and appointments I made during the closed season and would like to apologise sincerely to all supporters, Port Vale staff and the wider Burslem community for the impact of my decisions last summer.
"The three managers under my watch have had my full and unwavering support both financially and with full autonomy. When considering Bruno [Ribeiro]'s replacement I interviewed a very successful established manager who stated that my loyalty to the people I employ was my Achilles' heel, something which may have contributed to where we find ourselves today.
"I have had a modicum of success in my business life and when I endured setbacks, of which there were many, I used to dust myself down and get back into the project in hand. Under normal circumstances that's how I would be thinking today wanting to roll my sleeves up, plan and fund our way back to League One next season. Sadly, due the environment of the last few months, I do not feel that is now possible.
"It is with a heavy heart that I have decided to stand down as chairman with immediate effect and relinquish all remaining duties that I am involved in. I will leave it to Colin Garlick the club's CEO, and the team he is building, to work through what will be a very difficult period for the football club.
"I will not be making any further comment or statement until the football club is sold but will endeavour to ensure that the right party purchase the club. I will also not be attending any games at Vale Park going forward. All that I ask is that you, the supporters, please put any differences that you may have behind you and try to fully support your club as it will need you now more than ever."
Vale are expected to make an announcement regarding a full-time manager this week, with Michael Brown's deal only lasting until the end of the season.