In a 35-minute press conference, Woods also denied taking any illegal drugs and said his Swedish wife, Elin, would not be attending the tournament.
Woods was facing questions from a group of reporters for the first time since crashing his car into a fire hydrant outside his Florida home on 27 November 2009.
The incident sparked a series of revelations about the American's private life and led him to admit he had "had affairs and cheated".
Woods looked tense and nervous as he arrived to face the 180 assembled journalists at the Augusta media centre, although his demeanour was broken by an occasional smile.
After thanking the spectators who had watched his practice round on Monday, he apologised to his fellow players for the distractions of the last few months.
"I know the players have been bombarded by questions and I hope after today they can be left alone," he said.
"I apologise to them for having to endure what they have over the last few months."
When asked what had been the most difficult thing about recent months, Woods said: "Having to look at myself like I never want to look at myself, how far astray I got from my core fundamentals and morals my mom and dad taught me.
Only 180 accredited journalists were allowed to attend the news conference
"The other difficult part has just been the constant harassment to my family and my wife and kids being photographed everywhere they go."
Woods will be bidding to win his 15th Major, drawing him closer to Jack Nicklaus's record of 18.
Yet he insisted that winning tournaments was "insignificant" when compared to the "damage" he had caused his family.
"The fact I won golf tournaments is irrelevant and unimportant compared to all the damage I've done," he said.
"I hurt so many people close to me and I lied to myself - it's pretty brutal. I take full responsibility for what I have done."
This "hurt" included missing his son Charlie's first birthday in February in order to complete 45 days of therapy for a condition he would not specify, believed to be sex addiction.
"I missed my son's first birthday and that hurts a lot," he said. "That was very bad, that day. That was something I regret and probably will for the rest of my life."
I've never taken any illegal drug, ever
Only specially accredited journalists were allowed to attend the news conference at Augusta's media centre.
Whereas he had simply read a pre-prepared statement in February when making his first public appearance following the sex scandal, Woods, who has also been interviewed by ESPN and The Golf Channel since his misdemeanours came to light, now faced some truly probing questions.
He was asked whether he had taken human growth hormone (HGH) to aid his recovery from reconstructive knee surgery in 2008.
While Woods admitted he had worked with controversial Canadian doctor Anthony Galea, now the subject of federal investigations in his home country, he vehemently denied ever taking HGH.
"He (Galea) never gave me HGH or any PEDs (performance-enhancing drugs)," Woods insisted.
"I've never taken that in my entire life. I've never taken any illegal drug, ever, for that matter."
Faldo believes Woods will struggle
Galea was the man Woods went to because "he's worked with so many athletes (and) there's a certain comfort level to that when a person has worked with athletes".
Asked if he was now part of the investigation into Galea, Woods replied: "Yeah, they contacted Steiny (his management agent Mark Steinberg) and will get full co-operation whenever they need me.
"But as of right now, they have not asked for my time."
Before the scandal broke, Woods could be evasive and monosyllabic when facing the media.
Yet here he was open and almost effusive. The only question he failed to answer fully was how he had kept his cheating secret from his wife.
And Woods insisted he would change his behaviour on the course, as well as off it. The American, whose last tournament was the Australian Masters in November, has often been bad-tempered on the course.
He said: "I'm going to try to not to get as hot, but that means I won't be as exuberant.
"I made a decision to try and tone down my negative outbursts and be more respectful of the game."
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