Drayton are preparing for life in the Midland Premier after finishing bottom of the Northern Premier League First Division West.
Snape has taken the reins having jumped ship from fellow step-five side Uttoxeter Town, and he will be joined by an almost-entirely new squad at Greenfields.
"I'm not going to speak too ill of the previous squad, but I had a conversation with Mick (Murphy, chairman), and we had a look at what players were available and had decided to stay," said Snape.
"Only one lad from last season had decided to stay and fight for the cause, and that says a lot to me.
"That says obviously a few lads weren't bothered last year and have no willingness to pull the club out of the mess they've put it in themselves.
"It isn't Mick who's put the club where it is, or the fans, it was the players turning up and not making the effort.
"Now, the club has been relegated and there's no players around.
"It's a shame players have just gone and looked elsewhere, but I also get it at the same time, so I won't speak too ill of them.
"Players have probably played at step four for three or four years, so do they want to drop down, probably not?
"If they can get a step-four club or top of step five and still pick up some money, that's what they're going to do."
Snape admits Drayton will have a modest budget compared to some of their Midland Premier rivals, but pre-season training has already seen them welcome 40 prospective players.
Snape is excited over the potential at Greenfields, having quickly been convinced to make the switch from Uttoxeter.
"I'd been out of football for a bit, but last year, about November time, I had a phone call with Uttoxeter," he said.
"They were only on three points and the manager had left due to ill health, so I went in there and did a bit of a rebuild.
"Some players had gone while a few weren't committed, so their main focus was just to sustain themselves in step-five football.
"It was hard work, but we got through it and finished fourth from bottom in the end and kept them in the league.
"I was still in conversations with them until the Monday night about plans for the new season.
"But on the Tuesday, Mick had rang from Market Drayton and wanted to have a sit down.
"And to be honest, on the Wednesday morning, I'd made up my decision that I wanted to move."