Aslef said its drivers were now considering taking action, including a potential strike, after a meeting with ScotRail management on Monday.
The appointment was designed to try and reach a pay deal against a backdrop of rising inflation and the cost-of-living crisis.
However, the union said the 2.2 per cent pay increase offer put forward by ScotRail, which re-entered public ownership last month for the first time in a quarter century, fell “well short of what drivers expected”.
Kevin Lindsay, Aslef Scotland organiser, said: “Aslef members who have kept the country moving throughout the pandemic have been presented with a derisory pay offer from ScotRail management, which takes no account of the cost-of-living crisis workers face.
“Scotland’s train drivers did not make the decision to consider industrial action lightly. Indeed, we have not had a single pay dispute with Scotland’s railway operators for 21 years.
"Yet, just one month into the Scottish Government’s stewardship of ScotRail, we are being left with no option but to consider action in response.”
Mr Lindsay added: “ScotRail and the Scottish Government must recognise that these key workers deserve a decent pay rise. They should return to the negotiating table with a much fairer deal that recognises the vital work our members do.”
Joanne Maguire, ScotRail’s chief operating officer, said: “It is very disappointing that we find ourselves at this stage with Aslef, despite ongoing talks and a very good offer being made. We have made a pay offer that recognises the hard work of our colleagues and the cost-of-living challenges faced by families across the country.
“We are still trying to recover from the pandemic. With customer numbers around one third below pre-Covid levels, it remains a very challenging time for Scotland’s railway.
“We have assured Aslef and our workforce that we remain open and committed to further discussions in order to resolve the dispute and move forward together to provide the safest, greenest and most reliable railway we can for Scotland.”