Top SNP figurehead Mackay, 42, resigned last week after shocking messages were published showing he had pestered a schoolboy for six months on social media, including offering to take him to dinner and trying to meet up with him.
The dad-of-two was said to have 'resigned verbally' - but opposition parties raised concerns about transparency, with both Scottish Labour and the Tories criticising the lack of a paper trail.
In 270 messages, published in the Scottish Sun, Renfrewshire North and West MSP called the boy "cute", asked him to dinner and asked that their conversations be kept secret.
On Thursday morning Mackay resigned and a statement was issued saying: "I spoke last night with the First Minister and tendered my resignation with immediate effect."
Critics suggested that a lack of a written resignation would 'impede' any attempt to review the situation in future.
However a spokesman for First Minister Nicola Sturgeon refuted the suggestion a resignation letter was necessary.
A spokesman for the First Minister said: "The Scottish Government acted swiftly, decisively and entirely appropriately when the details of this issue came to light.
"Derek Mackay is no longer a minister, and his resignation took effect immediately on it being offered.
"There is no requirement for a letter."
But Tory MSP Donald Cameron said: "The SNP Government has form for covering things up and refusing to reveal paper trails.
"But on this most serious of matters, the public will expect full transparency.
"It is astonishing there's no letter submitting the resignation, nor one accepting it.
"It's high time Nicola Sturgeon adopted a more open and accountable approach to this scandal."
A Scottish Labour spokesman added: "The lack of a formal resignation letter raises significant concerns over transparency and would impede any attempt to review the nature of the resignation in the future.
"It seems that the Government is more interested in keeping the public in the dark over this very serious matter than allowing for proper scrutiny."
A Government source told the Herald it was merely "custom" for there to be an exchange of letters, and there was no requirement for a Cabinet Secretary to write one or the First Minister to reply.
Mr Mackay has been suspended by the SNP, which is now investigating his conduct.
Police Scotland has also spoken to the boy and an older SNP activist pursued by Mr Mackay.