Carter, who is widely considered the greatest flyhalf to play the game, joined Kobelco earlier this year following three seasons in France with Racing 92 after guiding the All Blacks to their third Rugby World Cup title in 2015.
The 36-year-old helped Kobelco to a 55-5 victory over twice-defending champions Suntory Sungoliath in the final at the weekend and was then given the MVP accolade.
"It's a really proud moment for someone that has had such a long career and is getting to the end of that career," the three-times World Player of the Year told Kyodo News.
"But that's not why I play the game. ... It's not about individual awards like this.
"At the same time it's nice to know the hard work and sacrifice that I have put in this year has been recognised."
Carter had said when his move to Japan was announced, even though he had been offered a new contract with Racing, that he wanted to be closer to New Zealand.
Another attraction was that the seasons were also shorter than those in Europe and he felt that had helped him play at a level he felt he had been unable to get to for a decade.
"I've really got my running game back to where it was probably 10 years ago," said Carter, who is the leading points scorer in international rugby with 1598 in 112 tests.
"It's been a real strength of mine throughout my career, to have a real attacking mindset and be a threat with ball in hand and looking to attack space.
"I felt like I did that this season. I haven't played with that freedom for the last couple of years."
Carter signed a two-year contract with Kobelco and with Japan hosting next year's Rugby World Cup he said he was looking forward to having a such a lengthy off-season.
"I haven't had an off-season as long as this for a long time," he said. "I sacrificed a lot by coming here to play in Japan while my family has been back in New Zealand, so I'm looking forward to taking some time off rugby."
(Reporting by Greg Stutchbury; Editing by Amlan Chakraborty)
