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.
With Manchester City confirmed as champions on April 15, United required a point to seal a second-place finish.
Their 2-0 win at Leicester City on Saturday afternoon was a first in five but David Moyes' side have not recorded back-to-back Premier League victories since January 2017.
Jose Mourinho wanted the point that guaranteed Manchester United will finish second in the Premier League this season, and he got it - but not much else.
The away supporters paid near-constant tributes to former boss Sir Alex Ferguson, the 76-year-old now out of intensive care having had an operation on a brain haemorrhage.
Rabindranath Tagore Returned Nobel Prize in Protest Against British: Tripura CM
Mr Deb made these remarks at a function in Udaipur to mark birth anniversary of Rabindranath Tagore . Well, this is not the first time that Tripura CM Deb has made headlines over his freaky comments.
"We are the second best team in the Premier League, a fantastic competition with lots of good teams with six teams trying to finish first", said.
"We need a point to finish second", stated Mourinho.
"I can think of managers who would be building towards the big game that's coming up next week and he might have that at the back of his mind".
"I am not critical of the performance at all".
United, denied victory by the inspired form of West Ham goalkeeper Adrian, moved four points clear of third-placed Tottenham with one game left. "I have to say I have a top end staff and they have been really helpful". I'm not as sad as I normally am when my players end their careers because he is going to be with us and even closer to me than he was as a player. That's what the real thing was and we've got that job done. Both players were booked. It will be a summer of change for West Ham before the 2018-19 season.
"Marcus and Anthony played against Brighton, today was for Alexis and Lingard and Sunday is again for Martial and Rashford".
Subs: Hart, Evra, Fernandez, Obiang, Cullen, Hugill.