"I definitely feel the attention of the media globally now," said the 23-year-old, who last month joined English giants United on a four-year deal from German champions Borussia Dortmund.
"I'm a member of a great club at Manchester United. I think I can handle the pressure and am pretty confident I can adapt to the style of the Premier League," added Kagawa, who scored 24 goals in 56 matches for Dortmund, during a United news conference.
Kagawa's arrival is a boost for United, who were within minutes of retaining their Premier League title last season until a late winner on the final day for Manchester City in a 3-2 win over Queens Park Rangers saw their cross-town rivals crowned champions instead.
With City bankrolled by wealthy Abu Dhabi-based owners, and Champions League winners Chelsea, who recently beat United to the signing of French playmaker Edin Hazard, backed by Russian billionaire Roman Abramovich, fears have been expressed over Ferguson's ongoing ability to compete in the transfer market.
United also needed to strengthen their midfield given Darren Fletcher has still to recover from a bowel complaint and there are also concerns regarding the fitness of Anderson.
Midfielder Paul Scholes abandoned his retirement half-way through last season and, together with fellow Old Trafford veteran Ryan Giggs, has signed on for a further year with United.
But in Kagawa the Red Devils have a highly-regarded young player.
He helped Dortmund land successive German titles and scored 17 goals as they completed a domestic double last season.