Inagaki featured in all four of Japan's games during the 2014 end-of-year rugby union internationals with the first two matches being non-cap internationals against the Māori All Blacks. His official test debut came against in Bucharest on 15 November 2014 and he won his second cap a week later against in Tbilisi. Inagaki was selected in the Japanese squad for the 2015 Rugby World Cup in England. He played in all five games for Japan which included their big upset over South Africa 34–32 in Brighton. Japan finished the 2015 World Cup with 3 wins out of 4 games but failed to reach the quarterfinals. Inagaki was also selected in Japan's squad for the 2019 Rugby World Cup which was to be held in Japan. Inagaki helped Japan reach their first ever quarterfinals where they went on to lose to eventualwinnersSouth Africa 26–3. Inagaki scored a try in Japan's pool match against Scotland which was his first ever test try and also helped push Japan to a 28–21 win.