Everton manager Frank Lampard says his side have been "on the wrong end of a lot of bad decisions this season" after the nine-man Toffees were beaten by Brentford at Goodison Park.
Leeds' draw at home to Brighton earlier on Sunday meant victory for Lampard's team would have secured their top-flight status with two games to spare, but the narrow loss leaves them just two points clear of 18th-placed Burnley and one above Jesse Marsch's side, who have played a game more.
Dominic Calvert-Lewin got the faintest of touches to Richarlison's flick to give the hosts an early lead, but the dismissal of teenage defender Jarrad Branthwaite - which came moments after Richarlison's appeals for a penalty for a foul by Kristoffer Ajer were turned down - swung the momentum back in the visitors' favour.
"When you see that shirt pull [on Richarlison], that's a foul anywhere on the pitch," said Lampard, who is facing an FA hearing over comments made in the aftermath of last month's 2-0 defeat by Liverpool at Anfield.
"This 'clear and obvious' phrase, I don't know if it still counts but I think it's a nonsense. The decision is either right or wrong.
"Is a shirt pull a foul? Yes. Is it in the box? Yes. It's a penalty."
A Richarlison spot-kick in first-half stoppage time restored Everton's advantage after Seamus Coleman's own goal had levelled for the Bees, but Brentford dominated the second half and deservedly turned the game on its head through headers from Yoane Wissa and Rico Henry.
The Toffees contacted the Professional Game Match Officials Limited (PGMOL) after the Liverpool defeat to query why referee Stuart Attwell did not penalise a challenge on Anthony Gordon.
"It's hard," Lampard continued. "I have to represent the club, represent the fans that come here, and those small margins can affect our position.
"I do believe that penalty for the shirt pull means maybe 2-0 and 11 men, and I think we all know how that game goes."
The Toffees' woes were compounded late on when substitute Salomon Rondon was sent off for a two-footed lunge on Henry, but Lampard's side will be safe if they beat Crystal Palace at home on Thursday evening.
An impressive haul of seven points from three games had lifted Everton clear of the bottom three before Sunday's crucial game, and Leeds' failure to overcome Brighton at Elland Road meant survival was within tantalising distance for Lampard and his players - who were greeted off the team bus by thousands of Toffees fans prior to kick-off.
Both sides had opportunities to open the scoring in a blistering start to the match, the first of which was spurned by Richarlison after Brentford goalkeeper David Raya had clawed Gordon's clever flick into the forward's path.
Ivan Toney and Richarlison traded further chances, before Calvert-Lewin - making his first start since 9 April - got the slightest of touches to Gordon's driven free-kick to break the deadlock and ramp up the noise inside an already frantic Goodison Park.
The mood changed dramatically, however, when Branthwaite was adjudged to have brought down Toney as last man.
The red card shifted the momentum inside Goodison Park as Christian Eriksen curled a free-kick narrowly wide of the far post, before Wissa's whipped delivery was diverted into his own net by Coleman.
There was still time for another twist before the interval as Mads Bech Sorensen was adjudged to have tugged back Richarlison inside the Brentford penalty area, allowing the Brazilian to slam home the resulting spot-kick for his 10th goal of the campaign in all competitions.
Brentford boss Thomas Frank switched to a back three at half-time in a bid to press home his side's numerical advantage, and the bold move paid off as the visitors struck twice in the space of three second-half minutes.
There was little Jordan Pickford could do about Wissa's looping header or Henry's well-placed effort moments later, which handed Brentford a first league double in this fixture since 1936.
There seemed little chance of Everton clawing their way back into the game at this stage, but any hopes the Toffees had of salvaging an unlikely point were well and truly extinguished by Rondon, whose reckless challenge on Henry earned him a straight red card from referee Michael Oliver.
The victory lifts Brentford up to 11th - two points behind Leicester and Brighton in ninth and 10th respectively.