Sir Brian, one of the Yes campaign's leading supporters and an SNP donor, said nothing about the Scottish vote but his comment followed questions about potential renationalisation of the rail network if there is a change of government at Westminster.
"Within the company, there is more anxiety in some ways about the outcome of the next election," the Stagecoach chairman said: "We don't really see this (referendum) as a big issue for the company."
Shareholder and transport campaigner David Redgewell had urged chief executive Martin Griffiths, who leads the UK's Rail Development Group, to continue speaking up for the private operators, said: "We need to be wary of the Left, who are trying to drive us back to the dark ages of British Rail."
Mr Griffiths said: "I will continue both as chief executive and as chairman of the Rail Development Group to make the positive case for the industry, which is actually a victim of its own success. We do have some big challenges and some of the policies being advocated by the Labour Party are not going to address these challenges."
Mr Griffiths said: "We need a strong partnership between the Department for Transport, private operators and Network Rail to unlock some of the opportunities that are out there."
He said Stagecoach's extension to its South-West Trains franchise would not be signed before the election. Sir Brian said Mr Griffiths, who took over as chief executive in June 2013, was now leading the industry. "The team has been doing a great job here, it's like they have been doing it for 15 years but it is only 15 months."
Asked whether Stagecoach favoured operators gaining control of infrastructure from Network Rail, Mr Griffiths said the group had always believed in closer management of track and operations, as in its alliance with Network Rail in South-West Trains. "It is not right for everywhere," he said, but added: "You can make decisions quicker and react to disruption quicker, and ultimately get efficiencies over the longer-term. It is not about ownership of the assets it is about day to day management and we certainly believe in it."
Mr Griffiths earlier told shareholders the future of transport policy could hinge on the general election. "We look for it to be stable, to allow our businesses to continue the commercial model, and hopefully to have government fund long-term concessions and other areas where they invest in our business."
Asked whether park 'n' ride services had slowed down journey times, Mr Griffiths said the hub at Halbeath in Fife was a typical success story and the group would soon open its first wholly commercial park 'n' ride in Manchester. "It is about persuading people to get out of their car and on to a bus, reducing congestion and we think it has been successful," he added.
Ross Paterson, finance director, said last year's earnings per share growth of almost six per cent was a "fantastic result".