Jarrod Bowen scored a controversial stoppage-time penalty after a VAR review found Matthijs de Ligt had fouled Danny Ings to send United to a fourth Premier League defeat in nine games this season.
But the Red Devils missed a host of scoring chances before Casemiro’s header canceled out Crisencio Somerville’s opener for West Ham.
Alejandro Garnacho hit the post with a good chance, Bruno Fernandes headed over and Rasmus Hoylund and Marcus Rashford also missed decent opportunities.
But the main culprit was Diogo Dalot, who rounded Hammers goalkeeper Lukasz Fabianski before firing wide from the open goal from 12 yards.
The defeat saw United drop to 14th in the table, increasing the pressure on boss Erik ten Haag, and Argentina defender Martinez admitted it was difficult to accept.
“I feel very disappointed,” the 26-year-old told MUTV.
“I hate to lose and I hated to lose this, and at this club it’s not what we want. Expectations are certainly very high and we want to win every game.
“But now it’s time to accept it, be honest with ourselves and move on.
“I want the best for this club. I am sure this club will be at the top. We will do everything we can to put this club where it deserves to be.
“I’m so disappointed, to be honest, because I see every day our skills, our quality, and then those days when we finish a game, we lose, we miss a lot of chances and it’s hard to accept it, but we have to accept it. that’s it.
“Everyone is fighting and we are giving everything, but I think we have to give more.
“We have to know that football is a mental game and we have to keep believing and believing until the end and stay hungry.
“We played very well in the first half, but in the second half we fell. We conceded both goals and failed to win the game. I’m so disappointed, to be honest.”
Somerville, a half-time substitute, ran out to the duo to celebrate his first goal for the club with Mohamed Quddus suspended following his red card meltdown at Tottenham last weekend.
“I told Mo that when I come on I will score,” said the summer signing from Leeds.
“I’ve had to be patient at times this season, but when I come in I just try to energize the team. I think that’s why West Ham want me.”