The 28-year-old Briton, a 66-1 outsider at the start of the week, made the most of a stunning back-nine collapse by American Spieth to capture the coveted Masters green jacket at Augusta National on Sunday.
Willett does not believe he is yet at the same level as the "Big Three" but that is definitely where he wants to be.
"Guys like Rory, Jordan and Jason have achieved a bit more than me at this stage," he said in a European Tour news release on Tuesday.
"I still have a little way to go to be up there with those boys but it's a fantastic start and a big move in the right direction to start doing special things in the very biggest tournaments.
"I am looking forward to being part of that illustrious group of major winners, which still sounds a bit odd to be honest, but I want to keep moving forward with my career and seeing what else I can achieve," Willett said.
Now world number nine, he said he had no idea how good his game could eventually be and that "before Sunday people probably didn't think I was capable of what I achieved".
"It's a special feeling and one I want to feel a few more times," the Englishman said.
Willett, the former world amateur number one, will make his first appearance in Europe as Masters champion when he competes at the May 19-22 Irish Open that will be hosted by the Rory McIlroy Foundation at the K Club just outside Dublin.
"The Irish Open is going to be awesome," he said.
(Editing by Louise Ireland)
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