Williams also said that his sacking by Woods was poor reward for his loyalty to the golfer.
New Zealand Herald quoted him as saying, "Realistically, I could look back and say I've wasted the last two years of my life because he's played infrequently, he's been injured and he's played poorly."
He added, "I was prepared to hang in there through thick and thin, so I found the timing extraordinary."
Williams was the caddie to the former world number one golfer for the last 12 years during which the latter won 12 of his 14 major titles.
Stating that the fallout of Woods' marital infidelity was the toughest for him, Williams said, "I'm a stickler for loyalty, I stuck with Tiger through a difficult period when a lot of people thought I should have left his side when things weren't going as they should have been going."
Surprised at the timing of his dismissal, he said, "I'm not disappointed in the fact that I've got fired, I'm just disappointed in the timing of it, given how loyal I've been to him. That obviously didn't mean much to him."
Williams said that he was looking forward to work with his new employer Adam Scott and said, "I'm excited about it, the last few weeks carrying with Adam has kind of opened my eyes a little bit."