During an eight-year span beginning in 1958, Palmer won four Masters, finished second twice and third once. In his career, he wound up in the top 10 on a dozen occasions.
But he could never win two in a row because, he believes, he did not listen to his father.
"It could have been," Palmer said Wednesday on the eve of his 49th Masters appearance. "If I had done what my father taught me, I might have won five times in a row, because I had the opportunity to do that.
"He said, 'be tough, boy. Go out and play and if you list4en to anyone, you're not too smart. And play your own game. And if you start listening to other people when you're out there, I have a job pushing a lawn mower.'
"But I made some mistakes. If you make mistakes, you're not going to win three times in a row, or even two times in a row.
"When you walk off the 18th tee and you've got a one-shot lead and you're walking to the ball in the middle of the fairway to hit it up onto the green and two-putt for a win, and you walk 20 yards to the left to shake hands and talk to some old friend that wants to tell you how great you are, you're pretty stupid.
"And that's what I did. And that's why I didn't win two times or three times in a row."
Palmer actually bid the Masters farewell last year, believing it to be his last. Masters Chairman Hootie Johnson had imposed an age limit for former champions to play in the tournament, but when that standard was rescinded, Palmer made it clear he would return. Now he plans to play in one more Masters to reach the 50-year mark.
"You always think you can get a couple of good rounds in and that's the way I felt," he said. "I thought, well, it would be nice to do 50 Masters and that became kind of an objective of mine. That's the whole thing in a nutshell."
Palmer admitted he is not likely to do well this week because rainy conditions and a lengthened golf course have made the Augusta National course an extremely difficult test.
"Today (after three days of rain), it felt like the course was 1,000 yards longer than last year," he said.
Palmer, who turns 74 next September, said he found the course "very difficult" during practice sessions here.
"Where I used to hit a 1-iron and a 7-iron, I found myself using a driver and a 3-wood," he said. "Even the big hitters are a club or two more to most holes than what we did in days gone by."
Palmer said he and Jack Nicklaus, when they were Woods' age, would have given today's No. 1 golfer more of a battle than the current challengers have.
"There was certainly a tougher attitude and more playing to win versus today," he said. "There's a thing about the way the guys play today that is probably more you go to the office and you do your job. You do it in a work ethic style. You do that and if you win, you win, and if you lose, it's part of your job.
"I'm not sure that maybe there wasn't a little more emotion attached to it back in the earlier days of the tour."
Palmer said he pressed Johnson to change his decision to take away a lifetime exemption for the older champions, "because it was in keeping with the tradition of the tournament to have that lifetime exemption.
"I thought it was important that a player should decide when he should quit," Palmer said. "I should quit. I am getting to that stage. I am very aware of that and I will.
"But you heard why I am playing and I think it's only proper."