Dover started the new season on -12 points after failing to fulfill four fixtures in February.
They have lost all three of their matches so far to leave them rooted to the bottom of the table.
The Kent club went part-time in the summer and now only train twice a week.
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To make matters worse, Dover have a number of players out injured.
Town head to the Crabble Stadium this weekend with three wins and a draw from their first four fixtures.
“Chesterfield are a million miles away from us as a club,” Hessenthaler told Kent Online.
“It’s ridiculous this league. It’s not a level playing field any more, financially. We can’t compete with that.
"It’s totally changed to what it was four years ago.”
Despite three defeats on the spin, Hessenthaler is happy with their performances. So far they have lost 1-0 at home to Boreham Wood, 2-0 at Maidenhead United and 3-2 at Altrincham.
They hope to have centre-back Jake Goodman (concussion) back but Will Moses (knee), Marshall Wratten (ankle), Reda Johnson (calf) and Ryan Hanson (knee) remain out.
"When you only train once or twice a week and you are playing against teams who train every day, the likes of Chesterfield who we have got coming up, their fitness levels are going to be better than ours,” Hessenthaler explained.
“The problem we are getting is players are picking up injuries because they aren’t fit enough yet.
“Because we lacked a pre-season in terms of time on the training ground and that means they are playing catch-up and we aren’t training every day which doesn’t help.”
But the former Gillingham manager insists they won’t be sulking about it.
"That is what we are dealing with but we knew that and unfortunately we have got to deal with it,” he added.
"But if I thought it was a challenge which was pointless then we would be giving up and we are not going to be giving up.”