The 30-year-old hairdresser - whose brother, Grant, also died in tragic circumstances while just 25 - was laid to rest at St Andrew's Church in North Kilworth, attended by partner Simon van Herrewege and several family members.
Her parents Cilla and Paul did not attend the burial but were due to attend a subsequent funeral service.
More than £1 million has been raised for the Samaritans on Claire's Just Giving page following her death.
She was running the London Marathon for the second time when she fell to the ground on Birdcage Walk, near Buckingham Palace.
She had been treated by medical teams situated along the route before she was rushed to hospital, where she was later pronounced dead.
Van Herrewege said he was waiting to cheer Miss Squires over the finishing line when a nurse phoned to say she was “very poorly” and had been rushed to hospital.
“I thought she had twisted an ankle or something, and I ran and flagged down a taxi,” Van Herrewege said.
But when he arrived at the accident and emergency unit, he was informed that his girlfriend of nearly three years had died.
Claire was running to raise funds for the Samaritans in honour of her brother Grant, who died of a drug overdose in 2001 after becoming depressed over the death of his girlfriend.