The striker told the club's official website: "I'm so happy that we are safe because this club, the fans and everyone deserves to be in the Premier League".
In a boring game with few quality chances, United defender Luke Shaw came closest to scoring when he had a shot turned onto the post in the first half.
Mourinho opted to start Alexis Sanchez and Jesse Lingard up front against the Hammers, with Marcus Rashford and Anthony Martial benched.
The boring encounter flared up in the closing stages as West Ham captain Mark Noble clashed with Paul Pogba - the pair arguably lucky to only walk away with yellow cards.
Former United boss David Moyes was pleased with West Ham's display, even though they achieved their primary objective by securing Premier League survival last weekend. We have conceded a lot of goals this season so a clean sheet is great. We wanted to win and we want to move up the league if we can, but it's a good extra point.
"But when the game goes to 70, 75 minutes, you don't win, you don't lose, you do the job".
"But if you don't get the experience, you don't get the chance". We tried to organise the team to get that point but to give opportunities to players to play.
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United's league endeavours conclude on Sunday against Watford; but the priority now is, without doubt, the FA Cup final against Chelsea on May 19.
Mourinho has poisoned his own dressing room, as he did at Chelsea and Madrid, the rot hasn't set in completely yet but players who traditionally have been the corner stone of Old Trafford are being publicly being called out on the back of one start every couple of months.
"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".
The Frenchman had initially been chopped down by West Ham midfielder Cheikhou Kouyate which went unpunished by referee Jon Moss, with Pogba taking out his frustrations by deliberately tripping Noble.
"The last two games we have got two good clean sheets".
"I am not critical of the performance at all". "I have to say I have a top end staff and they have been really helpful".