Jenny Gilruth told ministers she understands the situation will be “deeply frustrating” to many but by drivers “choosing” to not work on their rest days, this makes timetabling “incredibly challenging”.
The minister said the situation with train drivers meant ScotRail were unable to run an “enhanced” service for the Nations League match at Hampden.
On Wednesday morning, ScotRail advised fans to leave the Scotland vs Armenia game early to get home as the last train back from Mount Florida to Glasgow Central will leave before the final whistle.
Ms Gilruth said ScotRail has advised there is no "sufficient” bus capacity to support transport of the crowds from Hampden to Glasgow that a “high capacity” train service would provide.
The drivers' union Aslef rejected the ScotRail’s latest 4.2% pay offer last week, but is expected to return to discussions tomorrow.
Ms Gilruth said she takes “absolute accountability” as the transport minister, however, said it would not be appropriate for her to be in the negotiating room.
Speaking at Holyrood during an urgent question on the football travel arrangements, the transport minister said: “Clearly we would all like to see the current pay negotiations settled so we can get back to providing a full rail service for passengers everywhere.”
Ms Gilruth said, due to the “wider industrial dispute”, the serious disruptions are “not of this Government’s making”.
The minister said: "The answer to this is to resolve the dispute and to that end I look forward to discussing with ScotRail after they meet with Aslef tomorrow.”
Responding after Graham Simpson asked the minister if she will apologise to the tartan army, Ms Gilruth said: “Traditionally, ScotRail do carry far more Scotland supporters to Hampden Games than return. Approximately, 7,000 fans travelled to the Ukraine match last week and only 2,500 travelled back as generally fans prefer to walk back to the city centre.
"It’s also worth saying that the crowd tonight is expected to be far smaller than the Ukraine game.”