Anas Sarwar insisted it was "not credible" that no-one had "taken responsibility" after a Holyrood report concluded the two women who made the allegations against the former first minister were "badly let down".
Ms Evans, the Scottish Government's most senior civil servant, came in for criticism over her role in the bungled handling of the harassment complaints, which saw Mr Salmond win a payout of more than £500,000 from the Court of Session back in 2019.
While Scottish First Minister Nicola Sturgeon is said to still have confidence in Ms Evans, Mr Sarwar said the committee report, published earlier this week was "unanimous in its views on the failures of government, and the failures of the permanent secretary".
The Committee on the Scottish Government Handling of Harassment Complaints said the handling of the two women's complaints had been "seriously flawed" and that the Scottish Government was responsible from an early stage "for a serious, substantial and entirely avoidable situation that resulted in a prolonged, expensive and unsuccessful defence" of the legal challenge brought by Mr Salmond.
The report complained that the Government failed to identify all relevant documents "fully and promptly" in the case, with this identified as an "individual failing" by Ms Evans, who knew about the prior contact the investigating officer had had with the women and did not ensure the relevant information was made available sooner.
The committee branded this as "unacceptable" and said those responsible should be held accountable.
Mr Sarwar said: "I think it is not credible for us to have gone through all of that situation and for no-one to have taken responsibility.
"I think there are still huge questions for the Permanent Secretary Leslie Evans. I think she has some serious thinking to do and should be considering her position."
His comments came after Mr Salmond announced he plans to take legal action against Ms Evans.
In a statement on Wednesday, the former SNP leader insisted such a move was necessary to "prevent a damaging erosion of trust in the institutions of Government".