The result leaving the Portuguese head coach demanding immediate improvement.
Soungoutou Magassa's late header cancelled out Diogo Dalot's earlier strike, extending United's inconsistent Premier League run and keeping them marooned in eighth place.
United entered the match on the back of a five-game unbeaten spell that had been punctured by a limp home defeat to Everton and only partially repaired by Sunday's comeback win at Crystal Palace. But any sense of momentum quickly vanished as the visitors frustrated them before striking from a corner in the 84th minute.
"It's frustrating, it's angry, that's it," Amorim said, delivering a blunt verdict in a tense press conference. When pressed on how the team can improve, he added: "It's working again and trying to win the next one."
The equaliser left him irate. "It's not going backwards," he said sharply when asked whether United had dipped in recent weeks. "The results are going backwards. We are really inconsistent. Look at the goal, 83 minutes, we have a long ball, everything is under control, and we need to do better."
Amorim, who admitted he would wait until Friday to speak to his players to avoid repeating past flare-ups, referenced his reaction to the 3-1 defeat at Brighton last season when he smashed a television in the dressing room. "I always have the feeling, I think everyone has the feeling, that we need to score more goals," he said. "Even against Brighton in October we were three-nil up and suddenly conceded twice. We suffer with that."
United's dominance had been patchy throughout. Alphonse Areola denied Bryan Mbeumo with a superb save, while Aaron Wan-Bissaka twice cleared off the line to spare the hosts before Dalot struck just shy of the hour.
Casemiro blocked repeatedly, Bruno Fernandes went close on several occasions and debutant Mohamadou Kante missed late on, but West Ham grew stronger as the game wore on.
Their manager, Nuno Espírito Santo, said his side fully merited the point. "I think it was a good performance overall," he said. "We created, we competed, we reacted very well even after we conceded. We dominated, we controlled, and it is well deserved that we got the draw."
Magassa's first goal for West Ham means the London club remain in the relegation zone but have collected two draws from their last three matches. United, meanwhile, travel to winless Wolves on Monday in urgent need of stability after failing to beat the team sitting 18th at home.
With inconsistency now the defining theme of their season, Amorim has made it clear that patience is running out.
Thomas Frank has said he is fully prepared to put emotion aside as Tottenham face Brentford on Saturday, insisting he will celebrate any Spurs goal despite hosting the club where he spent nine transformative years.
Gabriel Jesus is expected to reassess his Arsenal future in January after falling down the pecking order during a year dominated by injury setbacks.
Enzo Maresca admitted that Cole Palmer's long-awaited return was "the only good news" on a punishing Wednesday night for Chelsea, who were beaten 3-1 by a sharp Leeds United side at Elland Road.
When Thomas Frank returns to face Brentford, now as manager of Tottenham Hotspur, the stakes could not be higher.
