He said: "I think it was a very important game for us to start well and get three points against a very good side".
West Ham's former United striker Javier Hernandez was given a good reception before kick-off - a welcome certainly not extended to the visitors' on-loan Manchester City goalkeeper Joe Hart - but the Mexican had little else to cheer.
Mourinho later explained his decision to give away the medal, claiming it meant more to the child than to him.
It remains to be seen if United can match this level - or even surpass it - each week but the fans will have enjoyed the start to life in Mourinho's second season.More news: Kentucky mayor pushes to remove 2 Confederate statues
"I want to play West Ham a hard match, then go to Swansea for another hard match".
Five of West Ham's last six Premier League goals against Manchester United have come from set-pieces (one corner, four free-kicks). "Then we had a quality performance", he said.
There were plenty of positives for the United manager.
The reasons for Manchester United's excitement include the arrival of striker Romelu Lukaku for 75 million pounds ($97.42 million) from Everton, Chelsea's Serbia midfielder Nemanja Matic (40 mln) and Sweden defender Victor Lindelof from Benfica (30 mln).
But Matic's performance has been a real talking point on social media.More news: Trump faulted for not explicitly rebuking white supremacists
He added: "It depends on what is happening or what was happening behind doors and we don't know". I think every one of us is equipped to win the title.
"I'm really happy to be with them and I'm going to fight with them all the way, so let's go on Sunday".
"But we have players and if we cannot strengthen the team in these areas we have people we can trust and go for it".
Asked by MUTV if he could have hoped for more, Lukaku replied with a wry smile: "I wished to have three goals and a hat-trick to be fair, that would have been nicer".
Lukaku scored on his competitive debut for United in Tuesday's 2-1 UEFA Super Cup defeat to Madrid in Skopje and was named in Mourinho's starting line-up alongside Matic to make his Premier League bow against Slaven Bilic's side.More news: Stocks slide on continued concern over tension between United States and North Korea
A brace from their new £90m striker Romelu Lukaku, coupled with goals from substitute Anthony Martial and Paul Pogba, topped off the ideal day for Jose Mourinho's side as the quest to return to the summit of the English game began.
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