The German was a shock winner of her maiden major, beating world number one Williams 6-4 3-6 6-4 on Rod Laver Arena on Saturday.
Kerber, who was in her first grand slam final, was still struggling to come to terms with her success at her post-match news conference.
But the 28-year-old is eager to build on her dream win at Melbourne Park through the rest of the campaign.
"I think someday here it clicked again like in New York a few years ago [2011 US Open] where I reached the semis for my first time," Kerber said.
"Here it was like that. I was trying to believe much more in myself. When I won the first set, when I won against [Victoria] Azarenka, that shows me that I really am a good player and I can show it as well on the big courts.
"I was not playing very good last year on the big tournaments. This is the first big tournament of the year, and I won it, the first grand slam. It sounds crazy, but I can say I'm a grand slam champion now."
Kerber came through a tough contest against Williams, who committed 23 unforced errors in the first set before improving.
A 16-point sixth game in the deciding set proved crucial, however, as Kerber broke for a 4-2 lead.
It included a pair of stunning drop-shots and Kerber said the courageous moves were just part of her character.
"That's how I am, a little bit crazy, you know. I really know and I have confidence when I play my drop-shots," she said.
"I was, OK, the game is so long. I must change something what she was not expecting.
"I was really hoping the ball was coming over the net because they were like really good.
"When I hit the first one I said to myself, 'OK, make another one. You can do it'. It was just like more the feeling in this moment."