Moxon said his players were determined to beat Somerset in their final match starting at Headingley Carnegie today and promised they would not be giving up the ghost while survival remains an outside possibility.
Yorkshire will be relegated if they fail to beat Somerset.
However, even if they beat Somerset, they will still be relegated if Worcestershire claim at least 10 points from their remaining two games.
Worcestershire play Sussex at New Road today before rounding off their campaign against Durham at Chester-le-Street next week, with Yorkshire sitting out the final round of fixtures.
Although Yorkshire are down bar the shouting, director of professional cricket Moxon stressed they wanted to put on a good show for supporters who have backed them through thick and thin this year.
This time last summer, those supporters turned up at Headingley for the last game of the season with Yorkshire fighting to win the Championship for only the second time since 1968.
Yorkshire had to settle for third place on that occasion but they find themselves with an entirely different set of priorities going into the corresponding fixture this year, with the county battling not to finish first but to avoid finishing bottom.
Only five points separate Yorkshire from bottom-club Hampshire, who have a game in hand, and who conclude their campaign away to Lancashire this week and at home to Warwickshire next week.
“We want to beat Somerset and, wherever there’s life, there’s hope,” said Moxon.
“Clearly, we’ve got it all to do; we’ve got to win our game and then hope against hope that the other teams have really bad games.
“If, by some miracle, we do survive, it will obviously be happy days.
“But the important thing is that we put in a performance and try to win the game for all those people who have supported us this year.”
Moxon said he was heartened by the patience and understanding shown by the majority of members this summer.
He believes they appreciate the club’s ethos of trying to develop as many home-grown youngsters as possible – an ethos that runs from boardroom to dressing room.
“I think the vast majority of members understand what we’re trying to do and support what we’re trying to do,” added Moxon.
“They will be disappointed and frustrated at the moment, just like myself and everyone connected with Yorkshire County Cricket Club, but I’d like to think they can see the big picture.
“We went into the season knowing it was going to be a challenge and that everything would have to go well for us.
“We tried to go it alone, if you like, without an overseas player for much of the year, and the results show we are still a work in progress.
“But although we’re not the finished article by any means, I genuinely believe we’ve got the core of a very good team.
“Unfortunately, this year, we needed some of our players, some of our banker players, to perform, and we haven’t always had that.
“We’ve had countless strong positions that we’ve not capitalised on, and that’s been my biggest frustration really.
“Very rarely have we been totally outplayed, but we have consistently allowed positions of strength to slip from our grasp.
“Instead of getting 350 to 400, which we were getting last year, we’ve been getting 200 to 250, and we haven’t batted well enough on the result pitches at Headingley in particular.
“But when you look at our batting line-up for the long term, there is a lot of exciting potential there.”
Even if Yorkshire are relegated, Moxon said he would not be deterred from his dream of producing a successful Yorkshire side mainly comprised of home-grown players.
“My dream is to produce a team of predominantly Yorkshire-born players who will be successful for a long period of time,” he said.
“That is definitely my ultimate goal.
“At the same time, it’s a challenge and a long-term project.
“I knew there would be bumps along the way.
“But I firmly believe the majority of the squad are going to be excellent cricketers for Yorkshire for many years to come, and what we’ve got to do going forward is be a little bit more ruthless, a little bit more streetwise, and a little bit more careful along the way.
“This year, we’ve been too careless on too many occasions and we’ve been heavily punished for making errors.
“We need to learn our lessons for next summer, and I’m confident those lessons will be learned.”
Moxon made clear: “The frustration is that we all know how good we can be, but we haven’t shown that this year.
“We haven’t played well enough for long enough over the season, which is why we’re in the position we’re in.”