As it was, they shouldn't be too greedy.
"It certainly looks more like a Jose Mourinho team".
The left-foot finish and close-range header which introduced himself to the Old Trafford crowd gave Lukaku the flawless start. "I want to play West Ham on Sunday, a hard match".
Also, United need to avoid slumping out of form in the later stages of the Premier League, something that happened last season, finishing in sixth place. Potential champions? You wouldn't bet your mortgage against it happening.
Lukaku scores twice as Man Utd thrash West Ham
The Old Trafford faithful will want to thank Chelsea owner Roman Abramovich for selling Nemanja Matic to Manchester United this summer. His side will not get free pass against fellow Top 6 clubs, neither will weaker sides be ready to open themselves up and leave the space for Red Devils to exploit.
"The money that's been spent, his own personal expectations and what he's always delivered has been titles, so I would say United have to approach this season to win the league. But I now have a good group, a club much better equipped and much better organised in the areas that support the first-team squad", Mourinho told reporters.
West Ham offered little in attack with Javier Hernandez not enjoying his return to Old Trafford. He was one of the best central defenders in the last decade in the Premier League but he struggled. Romelu Lukaku is the marquee signing of Manchester United's transfer window.
United continued to press and were rewarded on 33 minutes when they broke from midfield as Marcus Rashford spotted the run of Lukaku in the area and the potential £90million man smashed in his shot off the inside of the near post. This time around Mourinho should give him more attacking-minded role and leave the more defensive work to Matic and Ander Herrera.
The Hammers were completely outplayed and could easily have trailed by more goals before substitute Anthony Martial and Paul Pogba finally put a more realistic slant on the scoreline in the closing minutes.
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Scott Tolzien went 2 for 5 for 24 yards, Phillip Walker went 9 for 20 for 86 yards, and Stephen Morris went 13 for 20 for 94 yards.