The Prime Minister’s former chief adviser made the comment during an explosive committee hearing that also saw him claim tens of thousands of people died needlessly during the pandemic.
Giving evidence to the Commons health and social care, and science and technology committees, Mr Cummings also claimed Boris Johnson suggested getting injected with coronavirus “live on TV” to show the virus was nothing to be worried about.
Mr Cummings accused both Ms Sturgeon and the Prime Minister of hindering efforts to halt the spread of the virus.
He said: "As soon as you had these meetings Nicola Sturgeon would just go straight out announce what she wanted straight afterwards.
“So you had these completely Potemkin meetings without anyone actually digging into the reality in detail, because everybody thought as soon as the meeting is finish everyone’s going to just pop up on TV and start babbling.”
Mr Cummings also hit out at the "intolerable" delay to a public inquiry, which the Prime Minister has set for spring 2022.
The former ally of Mr Johnson also said he could not imagine why Mr Johnson has not met bereaved families.
He said: “Tens of thousands of people died who didn’t need to die.
“There is absolutely no excuse for delaying that because a lot of the reasons for why that happened are still in place now.
“Look at the whole debate about variants and whatnot – this has to be honestly explained.
“If No.10 today won’t tell the truth about the official plan which they briefed the media about and described on TV a year ago, what on earth else is going on in there now?”
He added: “There is absolutely no excuse for a delay and the longer it is delayed, the more people will rewrite memories, the more documents will go astray, the more the whole thing will just become cancerous.”
Mr Cummings said he heard Mr Johnson say in October that he would rather see “bodies pile high” than impose another lockdown on the nation.
MPs also heard Mr Johnson did not take the virus seriously at first, dismissing it as the new “swine flu”, with Mr Cummings accusing the Prime Minister of even wanting to get the virus on television.
He said: “In February the Prime Minister regarded this as just a scare story. He described it as the new swine flu.
"The view of various officials inside No.10 was if we have the Prime Minister chairing Cobra meetings and he just tells everyone ‘it’s swine flu, don’t worry about it, I’m going to get Chris Whitty to inject me live on TV with coronavirus so everyone realises it’s nothing to be frightened of’, that would not help actually serious panic.”
Mr Cummings also turned on the Prime Minister, saying it was “completely crackers” he was in charge, and criticised the system that left him and former Labour leader Jeremy Corbyn as the options at an election.
He said: "Any system which ends up giving a choice between two people like that is a system that has obviously gone extremely wrong.
“There’s so many thousands and thousands of wonderful people in this country who could provide better leadership than either of those two.
“And there’s obviously something terribly wrong with the political parties if that’s the best that they can do.”
Mr Cummings also said “in any sensible, rational government” he would have not had the power he did.
“It is completely crazy that I should have been in such a senior position in my personal opinion,” he said.
“I’m not smart. I’ve not built great things in the world.
“It’s just completely crackers that someone like me should have been in there, just the same as it’s crackers that Boris Johnson was in there, and that the choice at the last election was Jeremy Corbyn.
“It’s also the case that there are wonderful people inside the Civil Service, there are brilliant, brilliant officials all over the place. But the system tends to weed them out from senior management jobs.
“And the problem in this crisis was very much lions led by donkeys over and over again.”
He explained the UK Government “didn’t act like it [Covid] was the most important thing in February, never mind in January”, adding it was not on a “war footing” and “lots of key people were literally skiing” in February.
Mr Cummings also told the committee that nations, including Britain, “completely failed” to see the warnings about the coronavirus pandemic.
The former Vote Leave convener also told MPs he was “completely baffled” as to why No.10 denied that herd immunity had been the official plan.
He said: “It’s not that people were thinking this is a good thing and we actively want it. It’s that it’s a complete inevitability and the only real question it’s one of timing. It’s either one of herd immunity by September or it’s herd immunity by January after a second peak.
"That was the assumption up until Friday, March 13, .”
Mr Cummings accused Matt Hancock of lying, and said the health secretary was “completely wrong” on March 15 last year to say herd immunity was not part of the plan.
He added: "The Secretary of State for Health should have been fired for at least 15-20 things, including lying to everybody on multiple occasions including in cabinet meetings and publicly."
MPs also heard Mark Sedwill, former head of the Civil Service and Cabinet secretary until June last year, had suggested telling people they hold old-fashioned "chicken pox parties" to generate herd immunity.
He also told MPs that planned Cobra security meetings had been changed after a request from US president Donald Trump to be involved in a Middle East bombing campaign and demands from the Prime Minister’s fiancée Carrie Symonds over a story about her dog.
Mr Cummings added: "Part of the building was arguing about whether we were going to bomb Iraq, part was arguing about whether we were going to quarantine or not, and the Prime Minister’s girlfriend was going crackers about something completely trivial."
Mr Cummings also dismissed claims the government put a shield around care homes as “complete nonsense”.
He said: “We were told categorically in March that people would be tested before they went back to homes. We only subsequently found out that that hadn’t happened.
“Now while the government rhetoric was ‘we have put a shield around care homes and blah blah blah’, it was complete nonsense.
“Quite the opposite of putting a shield around them, we sent people with Covid back to the care homes.”