Romelu Lukaku celebrates scoring his first ever Premier League goal for Manchester United, on his league debut. Photo: Reuters/Jason Cairnduff

MANCHESTER - Romelu Lukaku can attack his first Manchester United season under no pressure after scoring two goals on his Premier League debut against West Ham United, according to manager Jose Mourinho.

Lukaku, a £75 million ($97.6 million, 82.5 million euros) capture from Everton, netted United's first two goals as Mourinho's men cantered to a 4-0 home win in their opening fixture on Sunday.

Having scored in United's UEFA Super Cup loss to Real Madrid, he has three goals in his first two official games for the club and Mourinho said it would expedite his adaptation to life at Old Trafford.

"He scored in the Super Cup, he scored today. He's playing well, he's working hard. He likes the team, the team likes him," Mourinho said.

"For any striker, they can play phenomenally well, but if they don't score goals, the pressure is on them.

"So good for him, good for (Everton's) Wayne Rooney, for (Arsenal's Alexandre) Lacazette, for (Chelsea's Alvaro) Morata, for all the guys arriving in new clubs and scoring goals on the first day.

"It's always oxygen, happiness and confidence for them. Romelu knows me well. He knows that sometimes strikers can play very well for the team without scoring goals.

"He knows that from me, no pressure at all. But today was good. Very effective, with the first goal especially."

Good first game! Happy with the win! @manchesterunited

A post shared by Romelu Lukaku bolingoli (@rlukaku9) on

Lukaku, 24, finished crisply off the post from Marcus Rashford's pass in the 33rd minute and climbed to head in a Henrikh Mkhitaryan free-kick early in the second period.

Late strikes by substitute Anthony Martial and Paul Pogba gave United their biggest opening-weekend win since a 5-1 rout of Fulham in 2006 and sent them to the top of the fledgling standings on goal difference.

Mourinho, however, was eager to point out that despite a 3-1 win at Bournemouth in their opening fixture a year ago, United had finished the season in sixth place.

"Last season we were also top of the league in the first match and we finished sixth, so this means nothing," said the Portuguese, whose side visit Swansea City on Saturday.

"I want to make it clear. This just means we played well and with confidence levels really high and now our challenge is to keep these confidence levels.

"The fans have reasons to be optimistic, because we also are optimistic. But for me, (with) years and years of experience, and experience in the Premier League, my feet are on the ground and I'm calm."

While Nemanja Matic also excelled on his home debut, there was no place in the squad for United's third new signing, Swedish defender Victor Lindelof, but Mourinho said he would be eased into action gradually.

"I think Victor needs a little bit of time," the United manager said. "He's going to have that time."

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