He had been offered a promotion to become the Prime Minister’s chief of staff, but a leak of that news prompted a backlash within the Tory ranks – reportedly including Mr Johnson’s fiancee Carrie Symonds – which effectively forced Mr Cain out.
Mr Cain is reported to have sought the promotion to chief of staff after former journalist Allegra Stratton was made Downing Street’s television spokesperson – a move that would have sidelined him as communications director.
Sir Keir said that the public will be wondering why Number 10 is “squabbling” in the midst of the pandemic.
The Labour leader told LBC: “This is pathetic. I think millions of people will be waking up this morning, scratching their heads, saying what on earth is going on?
“We’re in the middle of a pandemic, we’re all worried about our health and our families, we’re all worried about our jobs, and this lot are squabbling behind the door of Number 10.”
Sir Keir added that Downing street needed to “pull themselves together”.
“It’s pathetic”, he said.”Pull yourselves together, focus on the job in hand.”
Following Mr Cain’s resignation, leading Tories have been quick to brush aside rumours of infighting.
Communities Secretary Robert Jenrick told BBC Breakfast: “It’s understandable that journalists, in particular, will be interested in the personalities of who works as advisers within Number 10 Downing Street.
“But the Prime Minister runs the Government.
“He is surrounded by a good team, a strong team of advisers, and, of course, the Cabinet.
“Our sole focus in Government is trying to steer the country through the pandemic.”
Meanwhile, Cabinet Office minister Michael Gove was challenged in the Commons about who he sided with in the Downing Street power struggle.
SNP Cabinet Office spokesman Pete Wishart said the “faceless characters who actually run this country in Number 10 are at each other’s throats”, before referencing Boris Johnson’s fiancee Carrie Symonds and his senior adviser Doming Cummings.
Mr Wishart asked: “Whose side is he on – Dom’s or Carrie’s?”
Mr Gove replied: “I’m on the side of people from Aberdeen to Aberystwyth who voted to leave the European Union, who want us as a United Kingdom to make a success of these new opportunities (Brexit).
“I know the Scottish Government is a total stranger to behind-the-scenes intrigue and briefing wars, so I can imagine his shock and amazement to see things reported in the newspapers.”