Asked about the MI5 chief's comments, the first minister said he was "very worried" about a "lack of coastal and offshore protection".
He identified waters north of Shetland as an area of significant Russian activity.
"I don't think we've got nearly the presence in those areas that we require today," he told BBC Scotland News.
"There's an obligation on the United Kingdom government to make sure that the country is safe. And I don't think the defence posture of the United Kingdom enables me to have that confidence."
Scotland is home to the UK's nuclear submarine fleet at Faslane, west of Glasgow. The SNP wants those weapons to be removed, but is in favour of an independent Scotland joining Nato.
Swinney insisted that independence would not hamper Scotland's security, but rather give the country "more choices".
The SNP leader said he had "always been a believer in defence co-operation between Scotland and other countries", citing Canada joining the EU's SAFE defence programme, external.
Responding to the first minister's comments, a Ministry of Defence Spokesperson said:
"The first duty of government is to keep its citizens safe, and this government is investing £298bn over the next four years to ensure we can tackle rising threats.
"The Navy is helping to patrol Nato's northern flank, with this year's carrier strike group deploying to the Arctic and the high north.
"To tackle these threats, we're also investing in new frigates for the Navy and high-tech uncrewed vessels as part of our Hybrid Navy, backed by £1.5bn in funding."
Delivering a speech at the UN General Assembly, external last month, Burnham said his government would invest in defence and build up the UK's "hard power and deterrence".
He added: "But we will not play Russia's game of trading escalatory rhetoric. Unlike Russia, we do not seek confrontation."