The loss leaves them with 10 points from seven matches, the same as David Moyes had in his abbreviated one-season campaign at the club in 2013-14, although Moyes' team had a goal difference of 10-9 compared with Mourinho's 10-12.
Mourinho's men travelled to the London Stadium on Saturday boasting an enviable record against West Ham but came away chastened after a 3-1 defeat killed off any realistic hopes of a Premier League challenge before the end of September.
Manchester United's lamentable submission to West Ham United on Saturday emphasised what we already knew.
Elsewhere, goals by Jamie Vardy and Harry Maguire secured Leicester City's 2-0 win over Newcastle United, who have lost their opening four home games for the first time amid British media reports of a possible takeover fronted by Peter Kenyon, the former Manchester United and Chelsea chief executive.
"That was as bad as you've seen from a United team for a long time", Scholes told BT Sport.
"I think a team that comes with that mental fragility, after the bad result [against Derby] and to come here and in five minutes to be 1-0 down, is not good".
The relationship between the pair seems to have hit an all-time low
It came after the French World Cup victor implicitly criticised his manager's tactics, imploring United to attack more and as rumours continued to swirl linking him with a move to Barcelona.
Mourinho threw on Rashford shortly before the hour-mark and went close to pulling a goal back when Marouane Fellaini, operating in forward role, powered a header downward only to see Lukasz Fabianski pull off a fine stop.
"In the past we've seen managers relieved of their duties, that's what would normally happen", said the six-time Premier League victor.
They were also recently knocked out of the EFL Cup by Championship club Derby County. But on top of that, you have to get the players playing.
The focus will inevitably fall on Pogba after another anonymous display and Mourinho's decision to substitute him in the 70th minute was greeted by ironic cheers.
Or does a precedent need to be set with Pogba to ensure that player power does not prevail?
"It was an offside goal", said Jose.
Freeland postpones United Nations speech as NAFTA deadline looms
More light is likely to be shed on the enforcement of new labor standards and trade dispute settlement arrangements. Mexican-made products were hit by those actions, which were aimed at protecting USA producers from import surges.