It came as the First Minister faced a barrage of criticism over growing waiting times in the NHS and in mental health services for children and young people.
Carol Cunningham, 64, took to Twitter to criticise health secretary Humza Yousaf after finding out her telephone consultation with an expert in the cardiology department at Glasgow Royal Infirmary would not be until July 3, 2024.
Ms Cunningham said her original appointment to check her health was in good condition had been cancelled due to Covid.
It was revealed in the past fortnight more than 10,000 Scots have been waiting more than two years for treatment on the NHS, with almost 3,000 having endured a similar wait for an outpatient appointment. The figure was just 648 patients in a similar position a year earlier.
Coming under attack from Scottish Conservative leader Douglas Ross at First Minister’s Questions, Ms Sturgeon said there were “tentative” signs of recent progress in terms of NHS waiting lists.
The First Minister said of Ms Cunningham’s case: “In terms of the particular case cited in the media today, no, I don’t think that is acceptable and I know that a review of that particular appointment – which is a follow-up outpatient appointment, not a first outpatient appointment – is being undertaken and contact with the patient will be made.
"It is the case that waiting times generally and those waiting an unacceptably long time for treatment has increased over the past year.
"I’m afraid that is the impact of a global pandemic.
"We have over the past year seen further waves of Covid that has had a big impact on the number of appointments that can be done in our National Health Service.”
Ms Sturgeon added: “The pandemic obviously had a significant impact, but in terms of the statistics published most recently we are starting to see tentative signs of improvement.”
She later insisted waiting times were worse in England than they are in Scotland.
Mr Ross said waiting times had seen “a 16-fold increase in a year”.
He said: “This isn’t the NHS recovery her Government promised. Things are getting worse – far worse – not better, First Minister.”
He also raised the case of Alan Turner, from Kelso, who was told he would have to wait up to three years for knee replacement surgery in October.
The 70-year-old was offered private treatment in England, Mr Ross said, paid for by the NHS in Scotland.
Ms Cunningham told the Scottish Sun she thought her wait was “unbelievable”. She said she had tweeted the letter to draw attention to the “shocking waiting time”.
Elsewhere, Scottish Labour leader Anas Sarwar said 6,200 children and young people were on a mental health treatment waiting list when Ms Sturgeon became First Minister.
The figure is now more than 10,000, he said.
Mr Sarwar raised the case of an eight-year-old boy who was diagnosed with autism ten months ago, but was told he would have to wait to see a psychiatrist before medication could be prescribed.
“He is still waiting,” Mr Sarwar said. “In that time his condition has become worse, and he is begging for the medication – in his words – to ‘sort out my head’.”
Ms Sturgeon said the Government was investing to support health boards in delivering treatment, and there were “signs of improvement”.
She said the most recent quarter saw the highest ever number of children and young people starting treatment in mental health services.
Ms Sturgeon added: “There is still considerable work to do, but the investment we are making, the reforms that we are making within mental health treatment services are starting to deliver that improvement.”
However, she said ministers “cannot magic away” the impact of the pandemic.
Mr Sarwar said: "If mental health services are going to be taken seriously, we need reform of the referral and triage system.
"We need a mental health professional in every GP practice.
"And young people in every primary and secondary school need to have access to face-to-face mental health services.”