The total number of patients seen in December, including walk-in centres - was up by 983 to 17,078 last month.
Meanwhile, nearly two-thirds of respondents (65%) said the Government was managing the current pressures on the NHS badly, 38 Degrees said.
Increased demand has led to more people waiting longer to be seen at A&E over the festive period.
Speaking during first minister's questions at Holyrood, Scottish Conservative leader Ruth Davidson called on Ms Sturgeon to stop cutting hospital beds while Scotland is in the midst of a "flu crisis".
"However, we are of course sorry for any extended waiting times experienced by patients and their families during this exceptionally busy period".
Patients in need of emergency care during these hours are now taken to hospitals in Bristol and Taunton.
"Extra medical and nursing staff were employed in all key areas and extra bed space was opened at Blackpool Victoria Hospital".
Robison said: "Scotland's accident and emergency departments are continuing to outperform those across the rest of the United Kingdom - and indeed it is to the great credit of NHS staff that even at the height of these exceptional winter pressures, nearly eight out of ten people who attended A&E were admitted, transferred or discharged within the four hour target".
More than 5000 patients were forced to wait over four hours to be seen at accident and emergency departments between Christmas Day and Hogmanay, with hundreds others having to wait for more than 12 hours.
Thousands of patients are waiting in ambulances for hours as the hospitals lack adequate space.
Dr Liz Mearns, medical director from NHS England's regional office, said: 'It's important we protect young children from the flu virus and get them vaccinated now.
Staff have been faced with rising numbers of flu cases and respiratory illness, with 48 flu-related deaths in England so far this winter.
Health services in North Somerset, Bristol and South Gloucestershire are all experiencing high levels of demand and the NHS has announced a number of plans to cope with the extra pressure including postponing some non-urgent inpatient care, day procedures and routine outpatients until January 31.
"That's why we recently announced the largest single increase in doctor training places in the history of the NHS - a 25 per cent expansion".
"I said earlier this week, the health secretary said in the chamber, that we apologise unreservedly not just at winter but at any time of the year to any patient who waits longer than they should do for hospital treatment or doesn't get the standard of treatment that they have a right to expect and I do that again, unequivocally, today".
Prioritisation to implement the workforce strategy that has been agreed between the Royal College and the relevant arms length bodies. Behind each statistic is a patient waiting longer for care, often in distress, and doctors working under impossible conditions, exhausted and frustrated that they can't provide the compassionate and quality care they want to for their patients.