In a game of precious few clear-cut chances, Luke Shaw hit the post and Paul Pogba headed wide with United's best opening.
Nevertheless, United will have a chance to finish the season with silverware, when they face Chelsea in the FA Cup on 19 May.
However, they are likely to be very active in the summer transfer window as Mourinho looks to assemble a squad capable of winning the Premier League title next season. "We are behind him and praying for a full recovery".
West Ham forward Marko Arnautovic has expressed his desire to carry his good form for the Hammers into next season.
Both players grabbed hold of one another, but it was Noble who was arguably the luckier of the pair to only be booked following his angry reaction.
Mourinho was happy his side bagged the runner-up spot.
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"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 Mourinho.
Yes, United aren't playing the free-flowing football that we've seen from other Premier League sides this season but they've earned second place - and are favourites to win the FA Cup.
Overall, I am pleased with the players all round. 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".
"I had no view of the incident at the end [between Pogba and Noble], it was all good".
Obviously, when you know you need a point to finish second, and the game gets to 70-75 minutes, you have a point in your hand, you are not going to gamble to try to win, because you know a point is what you need for second position.
Supporters took to Twitter to praise the teenager about his display against the Old Trafford outfit and a number of them feel that he had played his best game in a Hammers shirt.
As it was, the point was all United required to make sure they will finish above Tottenham, the only club that was capable of catching them before last night.