The pressure on Mourinho is increasing after every matchday as the Portuguese tactician has seemingly run out of ideas to arrest a slide at United.
"If you want the truth I think it was honestly horrendous", said Shaw.
But United, who finished a distant second behind Manchester City last season, are going backwards on the pitch - licking their wounds after their worst start to a league campaign for 29 years.
"In the past we've seen managers relieved of their duties, that's what would normally happen", said the six-time Premier League victor. "There has to be improvements". "The hunger and desire to get against people just wasn't there".
And according to the Daily Star, Mourinho gave the short answer of "options, only options", when asked why the star was left out, suggesting he has fallen down the pecking order. "No VAR. Last Tuesday, VAR".
He scored West Ham's third and now has four goals in six Premier League matches.
"But the problem is, I don't think Paul Pogba is on his own if he's voicing these types of things".
Mourinho blamed the officials for West Ham's first and third goals, saying the opener should have been flagged offside and the move that led to the Arnautovic goal included a foul on Rashford. Whether he even starts will say much about his future so long as Mourinho remains in charge. "So OK this time it was a foul".
West Ham were rewarded on five minutes, when Mark Noble slid in Pablo Zabaleta down the right and the Argentine crossed for Anderson to flick the ball brilliantly past David de Gea with his heel.
An unlucky own goal increased their lead but even a superb strike from Marcus Rashford made little difference, with Marko Arnautovic scoring the victor. "The referee decides in the other way". That's not good enough. It was not good enough from a Manchester United team with all the talent we have.
'For many months people are asking for Martial, Martial, Martial, ' said Mourinho after the match, explaining his decision to axe Sanchez and hand the France global a rare Premier League start.
On the absence of his fellow Chilean, Pellegrini added: "I was surprised about no Alexis Sanchez".