Dier, Kane - as well as Gary Cahill and Jordan Henderson - were in contention to receive the skipper's armband by boss Gareth Southgate but last week, it was revealed that Kane had been given top responsibility at the World Cup in Russia.
However, Dier has said that Kane 'deserves' to be given the honour, but stressed that each of the 23-man squad must be prepared to act as leaders during the tournament.
In an interview with BBC Radio 5 live and talkSPORT, the 24-year-old said: "I wasn't disappointed. I'm very happy for Harry to be given the opportunity. I think it's fully deserved.
"One of the things Gareth said when he spoke to us was that he wants things to continue in the same way, where he has leaders all over the pitch, and hopefully I can continue to do that as well. I think it's important that the whole team, everyone has to share the responsibility between everyone."
Dier was selected as England captain for the goalless draw with Germany in November.