Brand new to KIA , this group, and posting on Chess.com - mistakes all around!
<-- Typical KIA formation
At move 4.d4 you have left the realm of the KIA.
In the KIA the d-pawn goes to d3 to support the e2-e4 push.. The pawn on d3 is one of the most defining aspects of the KIA. What you have played is basically a queen's pawn opening with a k-side fianchetto. When you take into account the play by Black, what you have is a type of reversed Modern Defense. Mind you, I'm not saying it's good or bad; just that it's not a KIA.
I cannot tell you where you went wrong in your game. I'm not a chess coach. I manage this group and the purpose of the group is to provide the resources (information) for members to build an opening repertoire based on the KIA.
I suggest you look in the group forum for the topic "KIA References"
https://www.chess.com/clubs/forum/view/kia-references
Each of the top 3 recommended books in the list is a link to a book club dedicated to that specific book which contains links to database versions of the games which are referenced in that book. Play through some of those games to see how the KIA is set up and how it is played against various Black defenses.
I also suggest that you join our vote chess games. We are just about due to start a new vote game. You can ask questions there as well as creating topics as you have done here.