The First Minister and SNP leader made clear that she did "not consider the launch of the app last week to be remotely satisfactory" as opposition leaders insisted the "chaotic scenes" that had followed were a "predictable disaster" from the Scottish Government.
She also confirmed that there would be no changes to Scotland's Covid-19 restrictions at this moment, warning that the nation's situation in relation to the virus is fragile.
Scotland now requires all those going to nightclubs, some football matches and other large events to prove they have had both doses of coronavirus vaccine, the app to go with the vaccine certification scheme was only launched some 12 hours or so before it came into force.
In the wake of the "chaotic scenes", Scottish Conservative leader Douglas Ross repeated his calls for the vaccine certification scheme to be scrapped.
He added: "People are messaging just now to say they are still putting in all of their details correctly and they cannot get the vaccine passport up on the app. So there continue to be issues days on."
The Scottish Labour leader, Anas Sarwar, said the "complete shambles" of last week's launch showed that the Scottish Government should "either change or ditch this system".
He told the First Minister:
Meanwhile, the Scottish Liberal Democrat leader, Alex Cole-Hamilton, said: "The launch was shambolic, thousands of attempts to access Covid ID cards hit the buffers."
Ms Sturgeon conceded: "The app didn't work as we intended it to do last week. There is no point me trying to say anything different.
"It is deeply regrettable but action was taken to resolve the issue, the issue in essence was the linkage between the app and the NHS systems. Action has been taken to address and resolve that."
Giving a statement to MSPs in Holyrood, she said the problem many had experienced was that the app was "unable to locate their vaccination record from the information that they provided".
This was "especially acute" just after it launched on Thursday evening and also Friday, the First Minister said.
She stated: "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. I apologise for that.
"The problem was not with the app itself but with the NHS systems that it links to.
Improvements were made to the system, and Ms Sturgeon said the backlog of people waiting for their information to be matched had been cleared by Saturday lunchtime.
But with Scotland facing a "potentially difficult winter" with Covid, she argued the vaccine certification scheme could help keep businesses such as nightclubs open.
Her comments came as she confirmed that coronavirus restrictions in Scotland would not be changed at the moment.
She added that while the recent drop in case numbers was "extremely positive" she warned that the position remains fragile.
Scotland recorded 2,056 new Covid cases in the past 24 hours and a further 21 deaths - taking the number of people who have died within 28 days of testing positive for the disease to 8,687.
A total of 998 people are in hospital with recently confirmed Covid-19, down three in 24 hours, of whom 65 are in intensive care, down six.
Ms Sturgeon said: "Overall, the position we are in now is much, much better than we had feared it might be this time last month.
"Cases have more than halved in the last four weeks and the number of people in hospital and intensive care is also now starting to decline."
She said cases in the past week had fallen by a fifth and the average of 150 people being admitted to hospital daily in the second week of September has fallen to fewer than 100.
Ms Sturgeon continued: "Given that cases are continuing to fall, we hope and expect that the number of people in hospital will decline further. We also expect that the number of people dying from Covid will reduce."
But she also stated: "The number of people in hospital with Covid now is still higher than it was in late August.
"And the pressure on our NHS remains intense."
The situation "remains fragile and potentially very challenging" as winter approaches, the First Minister said.