The First Minister said passengers were significantly disrupted and “lessons must be learned from it.”
Hundreds of people suffered delays and overcrowding as trains struggled to cope with the volume of passengers trying to get home on Saturday 24 August.
It happened on the final weekend of the Edinburgh Festival which coincided with a Scotland v France rugby match at Murrayfield in the capital.
Trespassers on a line near the city and three train alarms being activated by passengers added to the disruption.
Alex Hynes, who heads ScotRail and Network Rail Scotland, yesterday questioned the wisdom of staging the match that day and said Waverley or Haymarket stations might have to close during major events to avoid being swamped.
Ms Sturgeon, speaking at First Minister’s Questions, said: “The recent disruption to services, including on the last weekend of the Edinburgh Festival, where passengers were significantly inconvenienced due to services being overwhelmed by demand was clearly unacceptable, and lessons must be learned from that.
“A review by [the] ScotRail Alliance is currently underway to identify actions that will strengthen planning for future events.”
“We will continue to work with ScotRail to make sure that where improvements need to be made they are made.
“That is first and foremost in the interests of the travelling public.
Scottish Conservatives transport spokesman Jamie Greene said the incident was “an absolute disgrace to passengers who use ScotRail”.
Colin Smyth, his Scottish Labour counterpart, said: “Passengers suffered utter chaos.”
But the First Minister rejected calls from Mr Smyth to strip Abellio of its “failing” contract to run ScotRail “at the earliest opportunity”.
She said the Scottish Government would take decisions about the future of the franchise “in an orderly and responsible manner”.
Ms Sturgeon said ScotRail’s performance overall had improved this year.
Mr Hynes told a Holyrood committee on Wednesday: “I’m not sure it is wise for us to host rugby at Murrayfield at the same time as the busiest Edinburgh Festival weekend.”
He also asked: “Is it wise to keep Waverley and Haymarket open at the same time?
“It’s clear to me we’re going to have to manage this risk in a different way.
“We took many people into Edinburgh and clearly the numbers of people who wanted to travel back at the same time created some pressure on the system,” he said. “We let our customers down.”
Mr Hynes said “quota controls” might be needed on the busiest days, which ScotRail said could include special trains, ticket types and their availability, and restrictions such as day and time of travel.
He said ScotRail was continuing to get more trains, but the festival was also “only going to get bigger”.