Pukki scored twice in victory over Liechtenstein last night to reach the finals.
He told Viasat afterwards: "I've never been so excited about a contest like this. We've made history. The dream is from a young age to get to a final round, and now we are here."
Markku Kanerva, Finland's national coach, was also pleased.
"It was a mature performance today. The team played calmly and patiently with a lot of heart. It's a fantastic feat," he added.