In an interview for June's edition of Empire magazine, Moore recalled his early meetings with 007 film director Guy Hamilton.
Moore said that while he would be playing the same character they wanted to avoid "any deliberate" comparisons.
The interview, one of a series in Empire on Bond, came ahead of new Bond film Skyfall.
Starring Daniel Craig as 007 and directed by Oscar-winner Sam Mendes, the latest movie in the franchise will be released in October.
Scenes have been shot in London, Turkey and the White Corries in Glencoe.
The filming in the Highlands in February reportedly involved a car chase featuring Aston Martin DB5s - the same car driven by Connery in Goldfinger and Thunderball.
Talking about his early discussions with Hamilton about taking over from Scottish actor Connery, Moore said: "We talked about my approach to the character.
"The thing he wanted to avoid was any deliberate comparison to Sean, apart from the fact I was playing the same character.
"So I was never saying 'Martini, shaken not stirred'."
In her interview with Empire, producer Barbara Broccoli recalls how Connery exploded the traditional image of a movie's leading man.
Ian Fleming's books about the secret agent were adapted for film by Broccoli's father Cubby Broccoli and Harry Saltzman.
She said: "The typical British leading man used to be Trevor Howard or Leslie Howard - very polite and your classic gentleman.
"I think the real genius of Cubby and Harry was the fact that they didn't pay any attention to the typical class structure and they took someone who was a very real person and put him into this suit."
The magazine tells of "unsung hero" Yat Malmgren, a Swedish dance teacher to whom Connery turned to help hone his movement and gestures.
It also tells of Dr No scriptwriter Terence Young introducing Connery to his Savile Row tailors and then telling the actor to sleep in the suits.
Empire said the idea was to give the character the look of a man who had an eye for finery, but was more caught up in "life and death than ironing shirts".

15 February 2017 Last updated at 12:57 GMT
He particularly likes visiting the Wilko store, sleeping on rugs and saying hello to customers.
One lady even thought he was a statue as she passed him on the shelf!
George does have a loving home that he returns to every evening. But in the day, he just loves to shop!
Video courtesy of Nicola Williams

Takayuki Tanooka, 44, and his wife briefly left Yamato Tanooka by the side of the road on the northern island of Hokkaido on 28 May as punishment.
When they came back he was gone. A huge search was launched and the boy was found at a military base on Friday.
Yamato was taken to hospital but was discharged on Tuesday.
The case sparked a debate in Japan about parenting.
Mr Tanooka told broadcaster TBS in an interview aired on Monday: "I said to him, 'Dad made you go though such a hard time. I am sorry'."
"And then, my son said, 'You are a good dad. I forgive you'."
The boy was found on Friday morning in a hut on a military drill field, some 5.5km (3.4 miles) from where he was left as a punishment for throwing stones at people and cars.
He said he had lost his sense of direction from crying and walked for about five hours before arriving at the building where he was found, according to The Mainichi newspaper.
He slept between two mattresses and "met no-one".
He said he drank water from a tap at the facility but ate nothing for six days, the newspaper said.
When found, Yamato was lightly dehydrated, malnourished and had scrapes on his arms and legs but was said to be otherwise in good health.
Police have said they will not be pressing charges against the parents, local media reported.
Roger Moore has told how one of his first decisions before taking over the role of James Bond was not to use Sean Connery's famous phrase "shaken not stirred".
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George the tabby cat has become the local celebrity in the Kings Chase Shopping Centre in Kingswood, Bristol.
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The father of a seven-year-old Japanese boy who was found alive after six nights alone in a dense forest says his son has forgiven him.