He also branded those campaigning for Britain to leave as "bonkers, nuts and plain daft."
Speaking in Brussels on Tuesday, the former Socialist MP said, "I just wonder what ordinary people in places like Wigan, Widnes and Wolverhampton make of it all?"
MacShane, who was first elected in 1994 and served in government under Tony Blair's leadership, said that ahead of the 23 June referendum, the "political elite" were dominating the Brexit debate.
Despite polls saying the Remain side has a 10 per cent lead over the Leave camp, MacShane, a former BBC journalist and newsreader, admits to being "very apprehensive" about the outcome.
"My big worry," he said, "is that the public, who have been told for 20 years by the British press that the EU is a waste of time, will just turn round and vote to leave and say 'sod off, you sort it out.'
"My fear is that those not part of the chattering classes, people in Wigan, Widnes and Wolverhampton, will deliver what the Daily Express and Daily Mail will tell them and vote to leave."MacShane, who was in Brussels to promote his new book, 'Let's Stay Together. Why Yes to Europe,' says a Brexit will "deny rights and benefits" to the next generation.
"I am particularly concerned that the young will not come out to vote and this will be a massive shame. The Brexiteers are doing a great disservice to young people, including my own who are in their 20s, and also to those not yet born, by taking away the rights to travel and work in Europe that I have enjoyed in my life."
The Oxford-educated MacShane, who is based in London, said there was an "incredibly significant risk" of this happening if Britain votes to leave.
"Yes, there are lots of problems that need sorting out, including the mass movement of people and Syrian and Iraqi refugees. This has to be managed but you don't do that by shutting up shop and raising the drawbridge."
MacShane, a former Privy Council member, also took a swipe at former London mayor and leading Brexiteer Boris Johnson and his stance on immigration, saying, "Let's remember that Boris' great grandfather was Turkish."
He also pointed out that the new Mayor of London, Sadiq Khan, was the son of immigrants.
MacShane noted that the book, a follow up to his highly acclaimed political analysis 'Brexit - how Britain will leave the European Union', was not to make the economic argument for staying in or out of the EU nor to focus on "negativity", which he said had been a theme of the referendum campaign so far.
He also refuted claims by UKIP and other Eurosceptics that the EU was already a federal super-state, saying, "it is far from that."