In this specific position, it is a dead draw. Your pawns were not mobile and the opponent's king successfully blockaded your passed pawn. Sooner or later, he will eventually sacrifice his knight.
However, knight endgames with a pawn advance should regularly be winning. Even more so, when there are pawns on both sides of the board. The inferior part has the most drawing chances when pawns are on the same side and both his king and knight are active. You did not do anything wrong. Kasparov wouldn't be able to win this endgame against me (or you, for that matter).
Hope this helped. Indeed, knight endgames are not very common (2%), and a final body of theory is yet to be established!
I found myself in a king, knight, and two pawns versus king, knight, and one pawn endgame, and I couldn't win. I fumbled around for many moves until eventually my opponent sacrificed his knight for both of my pawns. I couldn't really find much about knight endgames in Google. Does anybody know if these are generally drawish? Or, alternatively, the strategy I should've gone for? Thanks!