The football-mad Labour MP for Eastwood, near Glasgow poured scorn on Roy Hodgson's underdogs in a briefing with Scottish reporters.
Murphy, whose current frontbench role is in international relations, had been discussing his new book, The 10 Football Matches That Changed the World, about momentous encounters, when he was asked about the independence referendum.
Scotland's dismal performance in the 1978 World Cup has long been credited as a factor in the following year's failed devolution referendum because it sapped national confidence.
Asked about the potential impact on September's vote of an England win in Brazil, Murphy said: "Well, it's not going to happen." Asked why not, he replied: "Because they're s***. You don't know anything about football.
"If they manage to beat Spain and Germany and Argentina then they'll have changed the rules of the sport. It won't happen. I think most people in Scotland are kind of relaxed about it."
Murphy last night tried to downplay the remarks as "light-hearted" and insisted he wanted England to do well, but the SNP accused him of being stuck in the past and "disrespectful".
England, who only narrowly qualified for Brazil, play their first match on June 14 against Italy in the sweltering Amazonian city of Manaus. Scotland did not qualify. England's other two Group D matches are against the much-fancied Uruguayans and Costa Rica.
Despite the bookies doubting England will even qualify from the group, manager Hodgson insists the team could still triumph.
Hodgson said: "I definitely don't think that we are favourites to win the tournament but I also refuse to believe we need to be written off.
"If these players can achieve what we see them achieve sometimes, then we have a chance."
Murphy's gaffe has echoes of the one involving former Labour first minister Jack McConnell.
One month before the 2006 World Cup finals, McConnell sparked a row by saying that as Scotland hadn't qualified he would be cheering England's opponents, such as Trinidad and Tobago. He admitted: "There are people who think that as First Minister I should be supporting England instead, but football is not about politics so I will not be."
The "anyone but England" mentality was criticised by McConnell's predecessor, Henry McLeish.
James Dornan, the SNP MSP for Glasgow Cathcart, said: "As Scotland fans are discussing our national team's improving form under Gordon Strachan - including the excellent result this week against Poland, and our chances of qualification to Euro 2016 - it is sad that Jim Murphy is stuck in a bygone era making disrespectful comments about our neighbours."
Murphy, 46, was the last Labour Scottish secretary, serving from October 2008 to the end of Gordon Brown's government in May 2010.
He then served three years on the opposition frontbench at Westminster as shadow defence secretary, and, since October 2013, has been the shadow international development secretary.
Murphy is demanding improved safety conditions for migrant construction workers in Qatar as the country prepares to host the 2022 World Cup.
Defending his comments, Murphy said: "This was a lighthearted, off-the-cuff remark. Most fans know that England will have their work cut out.
"I hope England do really well but it will be some going to win the World Cup when they're up against a Spanish team as good as Brazil of the past and an Argentinian squad at the peak of their powers. An English Messi or Xavi would be a real help."