The Hammers had been winning their final home game of the season 1-0 thanks to a nicely worked Stewart Downing goal in the second half.
The win and even a draw would have meant the Toffees could not realistically leapfrog the East Londoners, who would have all but cemented a minimum of 10th spot above their opponents in the table ahead of the final games of the season next week.
So when Leon Osman equalised it was not damaging to West Ham's league position, and the potential to earn an extra £3million in prize money.
But Romelu Lukaku's habitual goal against the Hammers in the 93rd minute did see Roberto Martinez's side leapfrog West Ham into 10th, much to the annoyance of most of the 36,000 people at Upton Park.
Two of those people were David Sullivan Junior and Jack Sullivan, who could one day inherit the club from their dad David, and they took to social networking site Twitter to reveal their frustrations at seeing West Ham once again throw away points at the death.
Jack said: "Another late goal, shame for our last game at home! Hopefully we can end the season on a win next weekend."
Another late goal, shame for our last game at home! Hopefully we can end the season on a win,next weekend.— Jack Sullivan (@jsullivanwhu) May 16, 2015
His older brother David was equally frustrated and called on the side to get over the problem while urging fans to stay behind the team.
He said: "Very annoying for another late goal costing us points.
"Hopefully we can rectify this short term (against) Newcastle and next season. Keep the faith."
Very annoying for another late goal costing us points. Hopefully we can rectify this short term newcastle and next season. Keep the faith— DA'VE SULLIVAN (@DaveSulley) May 16, 2015
It is easy to see why the Sullivans and Hammers fans are so frustrated with their side.
Including West Ham's 1-1 draw away to Everton in the FA Cup back in January, the late goal was the eighth time this season the Hammers have conceded in the last five minutes to throw away either wins or draws.
Five of those goals have come in injury time and if the Hammers had just held their nerve in those matches they could now be sitting a point ahead of Swansea in eighth place in the table.