Revd Gilbert Nisbet led tributes to the 82-year-old, describing her as a "kind and helpful" woman who was a "rock" to her family.
Mary, known as Rae, was found battered to death in the living room of her first-floor flat in Green Gates in Leven on January, 5.
Sandra Weir, from Leven, has been charged with Mrs Logie's murder.
Mrs Logie's son Derek said: "We would like to thank everyone for their kindness and support at this difficult time. We would ask that privacy for the family is respected as we grieve for our mother."
Speaking at the funeral, Revd Nisbet said Leven had not yet come to terms with Mary's death.
He said: "We gather today, a community shocked by the event which caused the death of Rae Logie, struggling to comprehend all that has happened here among us.
"Our service this morning is overshadowed by the terrible action which caused Rae's death, but we must not let this predominate our gathering, nor allow it to fester into bitterness in our hearts.
"Rae had a kind heart and she was always willing to go the extra mile to be helpful. She cared for those she assisted and continued to visit them after she retired.
"Rae was able to look back with quiet pride and genuine satisfaction on all that she did through her working life."
Revd Nisbet also spoke about Mrs Logie's marriage.
"Rae met Wattie when they were introduced by a mutual friend at a party, marrying after a short courtship and enjoying 33 years of a close, strong, supportive and loving marriage.
"They were always together, except when Wattie went fishing - Rae drew the line at joining him in that - and she missed him terribly after his death.
"However, she managed - showing that stubborn determined streak which was one of her characteristics.
"She even leant to drive, although she did have several attempts before passing her test."
