With the Hammers 1-0 down and the goal at his mercy, the £20.5 million summer signing hit the post from just over one-yard, drove his rebound against the upright again, before goalkeeper Simon Mignolet collected to clear the danger.
West Ham then conceded three more goals at the London Stadium, much to the dismay of manager Slaven Bilic.
“We spoke before the game and I expected the guys to put in the same kind of performance as they did against Spurs, with energy, organisation and teamwork, but it wasn’t to be,” Bilic, as reported by his club's official website.
“We were slower than on Friday night and they were quicker.
“We could have got the first goal and it would definitely have affected the game.
"We should definitely have equalised with that [Ayew] chance at the end of the first half, too, and then it maybe would have been different but it wasn’t good enough, especially in the second half."
Sunday's incident could be a setback to the confidence of the Ghana international, who only now seems to be rediscovering the form that saw him hit 12 goals for Swansea City last season.
The 27-year-old spent almost three months on the sidelines after picking up a hamstring injury on his West Ham debut in August last year.
On his return, he struggled for playing time and form, but has managed to net four times since returning from the Africa Cup of Nations in February.
Should Ayew miss out of the Worst Football Miss Ever, the chances are that he will grab the Miss of the Season 'award'.