The First Minister urged the "small number of people" affected to book an appointment again.
But Scottish Conservative leader Douglas Ross said people were still being turned away, despite advice changing earlier this week.
He said the communication from the Scottish Government had been "a mess" and called for mass vaccination centres.
It comes after experts at the Joint Committee on Vaccination and Immunisation (JCVI) updated their advice on how long people should wait between their second and booster doses, cutting it from six months to three.
Despite this, there have been widespread reports of eligible people being turned away.
Speaking at First Minister's Questions on Thursday, Ms Sturgeon said: "I'm very sorry to anyone who was turned away from a vaccine clinic yesterday."
She added: "Vaccination … is a clinical process and a clinical procedure. It has to be backed up by protocols.
"When advice changes, those protocols have to change. That is a process that normally takes a lot longer than this.
"It is being done more quickly, rightly and properly, because of the urgency of the vaccination programme.
"That is a process that health boards are now implementing to make sure that they are giving effect to that change in guidance."
Ms Sturgeon said Scotland had the fastest vaccination programme of anywhere in the UK.
She said: "That's not a credit to this Government, that's a credit to those working so hard in every corner of the country every single day."
But Mr Ross said only five regional health boards in Scotland have so far implemented the updated JCVI guidance, adding five plan to do so “soon”, but four have not given any update on the issue.
He said: "A year ago today, the UK became one of the first countries in the world to approve a Covid vaccine.
"Since then, ten million jags have been delivered to people across Scotland. I want to thank all the frontline staff and volunteers who have made that happen.
“But in recent days, people who tried to get a vaccine have been turned away.
“The SNP Government insists everything has been sorted, but we are still hearing of people being refused vaccines.
“This problem was avoidable if the Government put the proper protocols in place before making announcements. The lack of planning from the SNP Government has led to confusion when the public really needed clarity.
“Even though there is a backlog of close to two million people waiting to get their jag, we still don’t have a detailed plan from the SNP Government about how they will speed up the booster jag rollout at this critical moment.
“Nicola Sturgeon is in denial about the problems her government’s poor communications have caused and about the need for mass vaccination centres to accelerate the pace of the vaccine rollout.
“They must open mass vaccination centres, if not on the scale of the Hydro or P&J Live, then they should at least be looking at launching major clinics in town halls across Scotland.
“The SNP Government needs to show the same urgency to rolling out the Covid booster programme as was the case in delivering the first and second doses.”