The First Minister said identity is a “complex thing” and stressed an independent Scotland would still be part of the British Isles.
She made the comments during an on-stage conversation with the journalist Graham Spiers at the Edinburgh Fringe on Wednesday.
Ms Sturgeon was asked by a member of the audience about winning hearts and minds over to independence.
Speaking at The Stand's New Town Theatre, she said politicians have to try to “communicate with people in an open and straightforward and human way”.
She said: “It’s about trying to, I suppose, make the argument for independence on the basis of what it is as opposed to how people characterise it.
"So, this might surprise people, but do you know I consider myself British as well as Scottish.
"British is an identity that comes from being part of the British Isles.
"An independent Scotland will still be part of the British Isles.
"People talk about independence sometimes as if we’re going to cut ourselves off and float away up into the North Sea.
"We’ll still be part of the British Isles. An independent Scotland would still be part of the British–Irish Council that I go to right now as First Minister.
"Identity is a complex thing. Many people live in Scotland, are as Scottish as I am, but will have a very proud Pakistani or Indian or African identity.
"Independence – it’s about self-governance. It’s about whoever lives in Scotland, wherever they come from, whatever their identity it is, however multi-faceted and complex that identity is, it’s about those of us living here taking responsibility for the decisions that determine what kind of country we are.”