The comments came as the company's consumer division reported its best results for nearly a decade, suggesting that its £2 billion investment in sports television rights is paying off.
This drove a 9% rise in underlying pre-tax profit for the London-headquartered group's fourth quarter to March 31.
Chief executive Gavin Patterson said of September's referendum: "It is a matter for the Scots, first of all. We won't be interfering from that perspective."
He added: "We will continue to have a business in Scotland regardless of the outcome. We have got a number of big customer relationships."
Mr Patterson noted BT's role in delivering parts of the Government's programme to extend broadband to rural areas, highlighting its forthcoming work in the Highlands and Islands, which he said is "very exciting".
"We have got 7,500 employees in Scotland and we are used to working outside of England. We service customers in 170 countries around the world," he said.
Having focused on cost-cutting rather than top-line growth for several years, BT reported a rare rise in underlying revenue of 1.2% for the three month period and a 0.5% increase for the year.
Adjusted pre-tax profit amounted to £901m for the quarter or £2.8 billion for the full year, up 6% on the previous 12 months.
BT's consumer business posted a 9% revenue rise in the fourth quarter to nearly £1.1bn, which the company said was driven by a 24% increase in broadband and television revenue following the launch of BT Sport. BT Sport has rights to Scottish Premier League and Rangers football matches as well as a host of English Premier League games.
BT said that customer line losses of 49,000 for the three months were the lowest in more than five years.
The performance was better than the City had expected.
Richard Hunter, head of equities at Hargreaves Lansdown Stockbrokers, said: "Strong fourth quarter numbers added to what had already been an impressive showing from BT, such that there is much scope for appreciation of the full year results."
Investors sent BT's shares up 10.8p or 2.9% to 387.6p.
The shares have risen by more than a third over the last 12 months
BT has proposed a final dividend of 7.5p, up 15% on last year, taking the full year dividend to 10.9p, also up 15%.
The payment will be made on September 8.
BT said it would increase its dividend by 10% to 15% this year and next. It also said it would extend its share buyback programme.
The telecoms company said it now has three million BT Sport customers, including those watching via satellite, its own television service, online or via is mobile application.
Mr Patterson said that having a sports offering helped its share of net additions to the broadband market rise from 50% to 75%.
"It has had a positive impact on the consumer business and the way we are seen as a brand," he said.
"There is more of a buzz around BT than there has been for some years.
"That makes a difference. It opens us up to a wider number of consumers."
Mr Patterson said that BT would unveil new television content later this year.
But he indicated that it is not interested in moving beyond sports broadcasting.
"We are not looking to move out of sport in creating our own channels," he said.
He said that sport was a special case because of the difficulty of accessing content from other providers.
BT has spent an estimated £2bn on sports rights, and secured exclusive coverage of Champions League and Europa League football from 2015.
Mr Patterson said: "New content will include sport but will not just be sport," he said.
He said that BT is aiming for a "step change" in its customer services, with investment targeted at preventing faults and better responses when problems arise.
Mr Patterson said: "We have made strong progress this year. Underlying revenue, adjusted profit before tax and normalised free cash flow have all grown and beaten market expectations."