Kim Leadbeater was speaking after a commission set up by Mrs Cox before her death recommended that the UK needs a government-led national strategy to combat a problem which affects millions of people.
The final report of the Jo Cox Loneliness Commission found that nine million adults in the UK are often or always lonely and that loneliness is as harmful to health as obesity or smoking 15 cigarettes a day.
And it detailed how three-quarters of GPs say they see up to five patients every day who are lonely, and that loneliness is estimated to cost employers £2.5 billion every year.
Ms Leadbeater said: “Yes, government has got to play a part, that’s where policies are made and that’s where some of the money’s going to come from. But the great thing about this issue is that we can all make a difference.
“We can all go out tomorrow and knock on somebody’s door, catch up with a friend we’ve not seen for a while who might be having a tough time, and we can all make a little bit of difference.”
Speaking following the report launch in Batley, West Yorkshire, Ms Leadbeater said: “On a day-to-day basis it needs to come from us – every single one of us.
“I’m really embarrassed that I didn’t know my neighbours until Jo got killed.
“And I know everybody on my street now. Because what they did, they scooped me up and looked after me when I needed it, and that just shows you the power of community.”
Ms Leadbeater said her sister developed an interest in combating loneliness when she found herself feeling alone as a student at Cambridge University.
She said: “We all have this outside persona that everything’s great and we’re having this fantastic time but often it’s not like that.
“Jo and I were really close when we were growing up - we did everything together.
“When she went away to university, she entered this world of Cambridge, which was a very intimidating place for a working-class northern girl.”
But Ms Leadbeater said her sister would have wanted the report to move from words to action. “Talking about things is fantastic but let’s get on with it,” she said.
The cross-party commission was established by Mrs Cox when she was the Labour MP for Batley and Spen.