The First Minister, addressing MSPs in Holyrood on Tuesday as part of her weekly Covid-19 update, said NHS Scotland systems were to blame for the troubled launch rather than the app itself.
Vaccine certification became mandatory for large events and nightclubs on Friday at 5am, but enforcement of the scheme will not begin until October 18.
Ms Sturgeon said the problems faced by the app were “especially acute” on Thursday evening and Friday, and that she was “well aware” people found it “extremely difficult” to use the app.
She said: “I know this caused extreme frustration for users, who wanted to download the app as quickly as possible, and also for businesses and events organisers who were planning to test their certification arrangements over the weekend and I apologise for that.
“The problem was not with the app itself, but with the NHS systems that it links to.
“Essentially the high level of demand after the launch of the app, combined with an error in one part of the NHS system, meant that information wasn’t being sent quickly enough from the NHS system to the app.
“This also, for a period, caused problems for those requesting paper copies of vaccination certificates or seeking to download a PDF.”
The SNP leader went on to say the “initial backlog” of those waiting for the vaccine passport had been “cleared” by Saturday lunchtime and the Scottish Government would continue to monitor the performance of the app.
She said: “Covid certification remains, in the Scottish Government’s view, a proportionate way of encouraging people to get vaccinated, and also of helping large events and night-time hospitality to keep operating during a potentially difficult winter.”
Ms Sturgeon said around 380,000 Scots had downloaded the app as of midnight on Sunday.
Reacting to the statement, opposition parties hit out at the vaccine passport app’s launch, with Scottish Tories leader Douglas Ross labelling it an “utter shambles from day one”.
Describing the scenes around the country as people failed to gain access to their certification as “chaotic”, the Scottish Conservative leader said many people were saying they still could not access their details and repeated calls for the scheme to be scrapped.
He said: “What an avoidable own goal this was, First Minister.
"But in her statement today, what does the First Minister say? The scheme came into force as planned.
"So it turns out Nicola Sturgeon planned for this chaos, she planned for hundreds of thousands of people to try to download an app and fail.
"She planned for Scottish football clubs to ignore it, she planned for businesses to be up in arms, she planned for a scheme that was a shambles from day one.”
Anas Sarwar, the Scottish Labour leader, highlighting the news exclusively revealed in The Scotsman that COP26 attendees will not require vaccine certification, said this also proved the scheme was unnecessary and focus on increasing the rate of vaccination was crucial.
“The government’s vaccine passport rollout is a complete shambles,” he said.
"This was a predictable disaster and it is the consequence of an arrogant government forcing through its ill-thought through plans despite concerns from the public, public health experts, and businesses.”
Mr Sarwar also highlighted “equality issues” around the scheme, stating 20 per cent of Scots do not have a passport and 30 per cent do not hold a driving licences, both of which are required to access the certification on the app.
He said: “First Minister, you are making this up as you go along.
"So will you either change or ditch this system?”
Alex Cole-Hamilton, the new leader of the Scottish Liberal Democrats, also repeated his criticism of the vaccine passport scheme.
He said: “What little confidence existed crumbled on Thursday night. The launch was shambolic. Thousands of attempts to access Covid ID cards hit the buffers.
"The government has had a litany of tech problems during and before the crisis. Once again it cannot even get the very basics right.”
On COP26, Ms Sturgeon said: “We of course are working with UK Government, with the United Nations, in terms of the overall mitigations in place around COP26.
“There are arrangements around testing and other mitigations that those attending COP will be required to comply with.
“These are arrangements in which we are co-operating with others and I know all of us, for all sorts of reasons, want COP26 to be a success.”
During the update, Ms Sturgeon also confirmed there would be no changes to the Covid-19 mitigation measures in place.
She said a final decision on the continued requirement for school pupils to wear face masks in school will be made shortly and that it was possible the measure would be kept in place for longer “given the risks of the winter period”.
In total, a further 2,056 positive cases were confirmed in the 24 hours to Tuesday, with a test positivity rate of 10.3 per cent.
Hospitalisations have also dropped below 1,000 with 998 people in hospital with Covid-19, down three from Monday.
A further 65 people were in intensive care with the disease, a reduction of two from the previous day.
The First Minister also reported a further 21 deaths have been registered in the past 24 hours.
In total, 4,223,719 people have received a first dose of the Covid-19 vaccine, with 3,849,656 having also received a second dose.