Moxon conceded Yorkshire face a battle to beat the drop after they were thrashed by a Somerset side who sauntered to a target of 228 from 51 overs with 10.5 overs to spare.
It comfortably eclipsed Yorkshire’s previous worst 10-wicket defeat when Lancashire made 148-0 at Old Trafford in 1875.
Yorkshire sit seventh in Division One, one place above the relegation spots occupied by Worcestershire and Hampshire.
“It is a relegation fight,” confessed Moxon. “You can’t get away from that.
“We’ve got to pull ourselves together and come out fighting.
“It’s certainly not over by any means; there’s just over half the Championship season to go and a couple of wins would send us right up the table.
“But we’ve got to stop letting opportunities slip as we are doing at the moment.
“We’re playing well for parts of matches but failing to cash-in on good positions.”
This game epitomised Moxon’s frustration.
Yorkshire were well in control after reaching 305-4 on the opening day.
But a dramatic collapse of 6-53 in the final session saw them ejected for 358 – at least 100 below par on a typically benign Taunton surface.
Although they subsequently fought well to restrict Somerset to 452 in reply after the home side had been 257-0, Yorkshire ultimately paid for that first day disintegration.
Moxon was happier with the second innings effort, when Yorkshire made 321, but they were 224-3 at one stage and well placed to emerge with at least a draw.
The loss of three wickets towards the end of day three, however, gave Somerset the edge, Yorkshire going into the final day on 249-6, a lead of 155.
The visitors’ cause – already difficult – appeared practically impossible when Jonny Bairstow was caught behind from the third ball of the day after failing to add to his overnight 80.
Bairstow thus missed out on becoming the first Yorkshire player to score two hundreds in a match since Younus Khan against Hampshire at Southampton in 2007, Charl Willoughby inducing him to nick a delivery angled across him.
But Somerset’s hopes of a quick kill were snuffed out by Adil Rashid and Ajmal Shahzad, who batted for most of the morning session in a tenacious attempt to salvage a draw.
The pair added a painstaking 35 in 26 overs before Shahzad fell in precisely the fashion in which you do not want to fall while trying to salvage a draw.
He was run-out after Rashid turned a ball from Steve Kirby to mid-wicket and called him for a rapid but reasonable single, substitute fielder Jake Lintott swooping as Shahzad ran in a curve that took him away from the stumps.
Six overs later, right on lunch, Ryan Sidebottom became Kirby’s 500th first-class wicket when he was bowled by the former Yorkshire pace man to leave Yorkshire 296-9.
Rashid and Oliver Hannon-Dalby added 25 in 11 overs after the break before Hannon-Dalby was caught at first slip off Gemaal Hussain.
Rashid finished unbeaten on 51 from 145 balls with eight fours – a welcome return to form and a gutsy effort.
Defending a meagre target on a fast-scoring ground, one sensed Yorkshire had to strike early to have any chance.
But their one opportunity came and went when Marcus Trescothick, on five, nearly ran himself out.
Trescothick pushed Shahzad to mid-wicket and set off for a single, got halfway up the pitch and then changed his mind.
The former England man was well short of his ground when Hannon-Dalby, running round from mid-on, missed with the throw.
Reprieved and relieved, Trescothick knuckled down with Arul Suppiah to once more frustrate the Yorkshire attack following their double-century alliance in the first innings.
The openers scored at around five runs an over without really seeming to force the issue, driving crisply and nudging craftily.
Not until the cusp of tea was there a clear surge in momentum, two consecutive overs from Rashid disappearing for 29.
Trescothick deposited the leg-spinner for a straight six into the Sir Ian Botham Stand and three times cut him for four, Rashid, for the most part, dropping too short.
With just 133 wanted after tea from 33 overs, victory became a procession as Trescothick and Suppiah achieved the rare feat of registering two double-century partnerships in the same match.
Trescothick also scored his second hundred of the match when he incongruously edged Joe Root for four, his innings, for the most part, apparently flawless.
The left-hander reached the milestone from 89 balls but afterwards confessed: “I didn’t really click until I’d got about 80.”
Trescothick finished on 151 to lift his aggregate against Yorkshire to 885 runs in his last nine Championship innings at 110.63.
It also left him just 22 short of 1,000 for the season, statistics that dwarfed Suppiah’s 67.
n Yorkshire hope to have opening batsman Joe Sayers available for tomorrow’s Championship match against Sussex at Hove.
Sayers missed the Somerset game with a foot injury.