Luke Shaw, in search of his first goal for United, came within inches of breaking the deadlock, but his fierce half-volley was tipped on to the post by a scrambling Adrian's boot as the sides went into the dressing rooms deadlocked.
Mourinho explained that his squad rotation was merely to get minutes into his players with an eye to the FA Cup final meeting with Chelsea on May 19 and confirmed Martial and Rashford will return against Watford on Sunday. "I think we deserved that, the boys deserve that and to be the runner-up is not bad in a league of this dimension and this difficulty".
In United's first game since legendary former manager Alex Ferguson had to have emergency surgery on a brain haemorrhage, the visiting fans showed their support to the 76-year-old Scot with persist chants of "we all love Alex Ferguson".
No goals at the break, but plenty of chances for both sides here at the London Stadium.
Survival was only mathematically secured last weekend and West Ham remain in lowly 15th place.
Marko Arnautovic again looks in the mood for the east Londoners.
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"We try to organise a team to get that point but give opportunities to people to play".
Mourinho reacted to Friday's meek 1-0 defeat at Brighton by making eight changes with Marcus Rashford and Anthony Martial relegated to the bench despite the continued absence of the injured Romelu Lukaku. Against Brighton, at half-time I told the players they were going to lose and tonight at half-time I said we would win.
However, that failed to provoke an immediate response as West Ham posed the early threat.
Jesse Lingard forced West Ham goalkeeper Adrian into his first save as the visitors started to take control of the contest, with Sanchez drawing another stop before the Spanish keeper turned Shaw's follow-up strike onto the post.
Paul Pogba curled a couple of shots narrowly wide for Manchester United, and the France midfielder was booked in the dying stages for kicking out at West Ham's Mark Noble, who was also shown a yellow card as tempers frayed.