The first minister said people had a responsibility "not to let extremists divide us".
She was speaking at a tea party at Glasgow Women's Library.
The "legacy" event was one of more than 120,000 taking place across the UK as part of the Great Get Together campaign.
It was organised by Mrs Cox's husband Brendan on the weekend of the anniversary of her death.
Kilmarnock-born Thomas Mair shouted "Britain first" when he shot and stabbed the 41-year-old mother-of-two in her Batley and Spen constituency on 16 June last year during the EU referendum campaign.
He was later handed a whole-life prison sentence for her murder.
Ms Sturgeon said: "I remember vividly as everybody does the sheer sense of shock a year ago when the news came through that an MP had been attacked, then a bit later on the dreadful news that she had been murdered.
"That shock was personal for politicians but it was profound I think for all of us because it was a horrible, violent act, like so much else that happens in the world, and made us focus on the things that divide people rather than the things that bring us together.
"So Brendan Cox, Jo's husband, and the Jo Cox Foundation have to their great credit been really focused on trying to celebrate Jo's memory by getting people to focus on what unites us, not what divides us.
"Jo's maiden speech in the House of Commons had that memorable phrase 'we have more in common than anything that divides us', so that's a pretty good principle  or all of us to try and live our lives by."
She continued: "We live in a world where a tiny minority of extremists try to divide us through acts of unspeakable violence and we've got such a responsibility not to allow them to do that."
Nicola Sturgeon has urged people to unite in the face of terrorism at an event marking the anniversary of the murder of Labour MP Jo Cox.