Swinney said there had previously been “excellent cooperation” between the Scottish government and the Scotland office led by Murray.
But Alexander’s arrival coincided with his appointment as joint director of the Scottish Labour Holyrood election campaign to get Swinney out of office.
Swinney said at this point “relations soured significantly”.
The first minister added he had known Alexander for decades since the pair were students at the University of Edinburgh.
“I bear nobody any personal ill will, I’m not interested in that,” Swinney said.
“I am interested in improving the lives of people in Scotland.
“If I have to battle past a Secretary of State for Scotland that is making life difficult, then it just makes it even more difficult for me.”
The Scotland Office has been approached for comment.