Margaret Gleeson, 70, died two days after a hernia operation at Wigan's Royal Albert Edward Infirmary in October 2015.
Concluding an inquest into her death, Simon Jones ruled out neglect and said she died due to a rare complication.
But he said he wanted to highlight concerns raised during the hearing.
Mr Jones said he would write to both the hospital and the Department of Health about the issue of patient safety at weekends.
However, Wrightington, Wigan and Leigh NHS Trust said it did not believe weekend staffing levels were to blame.
"The trust does not believe that Mrs Gleeson's death was the result of any difference between the resources available and services provided at the weekend and those provided on weekdays," a spokesman said.
"The trust already complies with national guidelines in relation to weekend working and is actively involved in an ongoing pilot scheme investigating the possible benefits which might be derived from seven day working."
The trust said its own investigation had revealed shortcomings in "some aspects" of Mrs Gleeson's care, for which it offered its "sincere apologies".
The inquest, sitting at Bolton Coroner's Court, heard medics believed Mrs Gleeson's operation had been a success, but it was later discovered that internal tissue had been torn during the procedure.
Her condition then deteriorated.
When questioned about weekend staffing during the hearing, the trust's Dr Sadasivam Loganathan agreed it was "a major concern".
He said: "You don't give the same attention as the patient deserves."
Mrs Gleeson's son, Peter Gleeson, said: "I think if she'd had the operation on a Monday or any other time in the week it would have possibly been a different outcome."
Her daughter Julie Barnes added: "The surgeon himself said if she'd have been reviewed and it had been picked up on the Saturday, it would have been a totally different outcome."
Stephen Jones, of Leigh Day solicitors, said the family were "disappointed" the coroner did not find neglect had been a factor.
"Whether the different weekend working practice within the trust had any affect in Mrs Gleeson's case we don't really know," he said.
"But what we can say is that sufficient concern was expressed by the clinicians at Wigan to cause patient concern."

Justin Welby made the announcement after a meeting of primates from the Anglican Communion in Canterbury.
In the UK, an act of Parliament passed in 1928 allowed for Easter Sunday to be fixed on the first Sunday after the second Saturday in April.
However, this has never been activated and Easter has remained variable, determined by the moon's cycle.
Easter is the most important Christian festival, as it celebrates the resurrection of Jesus Christ following his death by crucifixion on Good Friday.
The archbishop said he was in talks with Pope Francis, Coptic leader Pope Tawadros, and the leader of the Orthodox church Patriarch Bartholomew.
Mr Welby said he hoped the change would happen "in between five and 10 years time".
"I would love to see it before I retired", he said, although he warned the first attempt to make such a change was in the 10th Century.
An Anglican source told the BBC there had been 15 attempts to agree a common date since then.
Easter is on the first Sunday after the first ecclesiastical full moon following the spring equinox, meaning it can be celebrated on a Sunday between 22 March and 25 April.
But the Orthodox church follows the Julian calendar, hence has later Easter celebrations compared with those of Western Christianity.
In 1990, the Vatican approved a proposal for a fixed date, which was subject to agreement with other Christian churches and governments. It has not yet been reached.
A coroner has vowed to raise concerns about weekend staffing levels at a hospital where a grandmother died after a routine operation.
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The Archbishop of Canterbury is working with other Christian churches to agree on a fixed date for Easter.