“I feel as happy as a kid at Christmas, as I'm celebrating an achievement that fills me with pride,” he told Sky Italia.
“I thank all my teammates in every squad I've played for. Titles with your club are important, but these individual records also make you feel very special.
“Destiny is extraordinary, as I hadn't remembered until I read it in the papers this morning, but my first goal was also at Siena.”
Inzaghi has scored 300 goals in all competition during his long career, 110 of them in the Milan jersey.
Inzaghi also wished to thank Carlo Ancelotti and hopes he will remain with the Rossoneri for another season.
“I don't want to keep repeating myself on Ancelotti, otherwise it'll get pathetic, but the directors are wonderful and will make the right choice.
“We know that with him we have reached three Champions League Finals and have seen how difficult it is for teams to get there.
“As for today, we proved that when Milan get their players back from injury, this is a very competitive side.”