The Labour leader's claim came in an audacious bid to grab the mantle of "One Nation" politics for Labour and with it the centre ground.
Mr Miliband used his keynote address to the Labour conference in Manchester to tell his "story" – who he is and what his values are – in a bid to convince voters he can become the next prime minister.
He insisted David Cameron had lost the right to claim "we are all in this together" because of the way he had governed, in particular his decision to hand tax cuts to millionaires while cutting services and benefits for the poor.
Mr Miliband made clear there were deep bonds between the people of Scotland and the rest of the UK.
"If you think about the people of Scotland and the Olympic Games, they were not cheering on just the Scottish athletes of Team GB, they were cheering on all the athletes of Team GB," he said. "That's what the SNP don't understand."
Meanwhile, Labour MPs have expressed concerns over Scottish Labour leader Johann Lamont's public spending review, warning it could alienate the middle classes the party needs to win back.