A largely forgettable game sparked to life with a late altercation between Hammers captain Mark Noble and United’s Paul Pogba.
United, denied victory by the inspired form of West Ham goalkeeper Adrian, moved four points clear of third-placed Tottenham with one game left.
It means Mourinho’s side will finish four positions better off than last year, which was the Portuguese’s first season at the club.
And although Mourinho said he felt “OK” about finishing second, he added: “I am not jumping around – that’s not my nature or my history. Manchester United are the same.
“The top four is obviously important but it’s better to finish second than fourth and it’s better to be second for months and months and months than losing that position and that control.
“We don’t celebrate second position but we are happy because for a few months, we realised it was impossible to win the league and, of course, the target is the second position.
David Moyes’ side remain 15th in the table after securing their survival against Leicester last week.
Despite West Ham’s attempts to generate an atmosphere at the London Stadium for this fixture – by adding huge concourse motifs of their former captains and record breakers – there were a large number of empty seats.
And the game was reflective of an end-of-season affair, with the only moment of note in the later stages being a confrontation between both sets of players following Pogba’s foul on Noble.
“It was hardly worth talking about [the incident at the end]. The referee handled it well,” said Moyes after the West Ham captain appeared to grab the French midfielder by the neck in a scuffle.
Referee Jon Moss booked both players, who were on friendly terms by the final whistle.
“I was watching the images and Paul and Noble looked in love. Hugs and kisses and changing shirts (at full-time). It was good. It was competitive,” said Mourinho.
Audition for Wembley?
While unwanted results in this fixture [a defeat and a draw] contributed to United missing out on top-flight titles in 1992 and 1995, there was no such importance placed upon this encounter.
With Manchester City confirmed as champions on 15 April, United required a point to seal a second-place finish and manager Mourinho instead appeared to use the fixture as an audition for a place in his FA Cup final line-up against Chelsea on 19 May.
Deploying a three-man defence, the Portuguese boss made eight changes to his starting XI from the one that lost at Brighton, reintroducing the likes of Phil Jones, Alexis Sanchez and Luke Shaw.
Captain Antonio Valencia created United’s best opportunity of the first period, which Hammers goalkeeper Adrian expertly parried from Sanchez before brilliantly deflecting Shaw’s blistering follow-up onto the post.
England midfielder Jesse Lingard also restated his case for inclusion at Wembley with a lively performance that carried threat without goals – Adrian repelling three of his efforts.
As the minutes ticked down, United appeared to settle for their point instead of chasing all three.