Torrance, father of 2002 Ryder Cup-winning skipper Sam, died on Friday at the age of 82.
Harrington enjoyed a remarkable run of form in 2007 and 2008 during which he won two Opens and one US PGA Championship and said he could not have done it without his former mentor.
"He was the greatest golf coach in the world and he was a father figure to me after my own dad passed away," the 42-year-old Irishman told the European Tour website.
"My Majors would never have happened without Bob. Not a chance. But I don't think anybody should have any regrets because Bob lived a full life."
Harrington missed the cut in the 143rd Open at Hoylake on Friday.
Fellow Irishman McGinley, coached by Torrance for more than 20 years, echoed Harrington's views.
"We have lost one of life's, as well as one of golf's, true characters," said the 47-year-old Dubliner.
"I feel blessed to have known Bob for many years and to have had him as my coach since 1992. Not only was he a world class golf coach, a fact recognised right across the game, but he was also one of my very favourite people in life."
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