The 32-year-old resigned with immediate effect on Tuesday evening after five months in charge and was followed out of Station View by his assistant boss Liam Ormsby.
“This isn’t a decision that has been made overnight, but there have been problems at the club since the early days of my time there,” he said.
“Having spoken to a number of managers, it seems that what I’ve had to deal with in five months at Railway is more than most gaffers have to go through in five years.
“There have been a number of issues that were out of my hands, but out of respect for the club, I won’t go into details.
“I think that in the long-term the club looks to have a bright future, but short-term, things are going to be difficult.
“I’m sad to leave, but I think it’s best for both myself and for Railway.”
Beesley exits with the Locomotives 17th in the NCEL Premier Division standings.
His last game in charge was Saturday’s 3-2 home defeat to bottom-of-the-table Barton Town Old Boys.
Appointed to the role of player-boss in mid-September, the former Harrogate Town striker brought about an upturn in fortunes at Starbeck, guiding the club out of the relegation zone following a difficult start to the 2016/17 campaign.
He oversaw nine victories and four draws during his 25 league games at the helm, scoring 10 goals in the process.
“I think that I’ve left the club in a better position than when I came in and I’m pleased about that,”Beesley continued.
“They are 15 points above the relegation places with a few games in hand now, which I feel is decent progress.
“There was a losing mentality when I arrived. The club had been relegated the season before and I knew it would be a tough job, but I maybe underestimated exactly how tough.
“As a manager, it’s fantastic when you’re winning, but very hard when you’re losing games.
“I want to thank the club for giving me the opportunity to manage them. There are some fantastic characters involved at Railway and I’m grateful for all the support that I’ve received.”
Beesley singled out October’s 2-1 victory at Armthorpe Welfare as the highlight of his time at Station View.
“That was my first ever win as a manager and a great feeling,” he continued.
“It was a night game and we went there with loads of players missing, only one substitute and a couple of 16-year-old kids in the squad.
“We were really up against it but we got the result and then kicked on a little bit from there.”