The fee for the 19-year-old, dubbed the new Thierry Henry despite barely 50 first-team games for the Ligue 1 side, was put at 36 million pounds ($55.
11 million) by British media and as high as 80 million euros ($90.27 million) by French media.
However, the forward told a news conference at France’s training camp in Clairefontaine on Wednesday that he was not concerned about the cost of the transfer.
“My family were definitely a bit nervous because of my high price but I’m going to stay focussed on my work,” he said.
“I’m not sure I’m worth 80 million euros. I left for the football side. It’s quite crazy for a player of my age but that’s how the market works. This sum has been negotiated between the two clubs.”
Martial does not believe his price tag will be a problem as he learns to adapt to the Premier League.
“I don’t see myself as being under any pressure. Since I was young, people have told me I have the right characteristics to play in England,” he added.
Martial said United manager Louis van Gaal had asked him his best position and been told it was in the centre.
“But he told me I can play in a number of positions,” the French Under-21 international added. “It’s the coach who decides.”
Nor did Martial appear overawed by the prospect of featuring alongside players like England captain Wayne Rooney.
“It’s normal Wayne Rooney doesn’t know me,” he said. “Next to him I’ll improve my game a lot.”
Martial, who scored nine goals in 35 league matches last season, has been called up by Euro 2016 hosts France for friendlies against Portugal in Lisbon on Friday and Serbia in Bordeaux on Monday.
(Reporting by Steve Tongue in London and Julien Pretot in Paris; editing by Ken Ferris)