Wales and Iceland have excelled in the competition despite this being the first time they have qualified.
Wales face Portugal on Wednesday in the semi-final, while hosts France eliminated Iceland in the last eight.
"I think there will be a boom in those countries and we will see more kids there playing football," said Kallen.
Northern Ireland, Albania and Slovakia also appeared in the competition for the first time.
"People were anxious the format might not work but it has worked," Kallen said. "We have seen two teams going further than anybody believed they would and that's positive."
Some have criticised the new format and the defensive approach taken by teams relying on draws to get through the group stage as a best third-paced side.
However, that also contributed to the exciting conclusion to the group stages with most teams needing points to qualify, typified by Iceland's thrilling late victory against Austria.
The new format will be in place for Euro 2020, which will be hosted throughout Europe, and Kallen said it could also be adopted beyond that.
The decision to expand the European Championships from 16 to 24 teams has been "very positive", tournament director Martin Kallen has said.