The party's leader in Northern Ireland Michelle O'Neill says James Brokenshire did not take their calls on board.
Under Northern Ireland's power-sharing agreement, the government must be run by Irish nationalists and unionists together, with the largest party being invited to put forward a candidate for first minister.
Mr Brokenshire met all the party leaders on Monday in a bid to restore the power-sharing executive.
A Sinn Féin delegation left a brief meeting with Secretary of State James Brokenshire on Tuesday as they were unhappy with progress on legacy issues.
She added: "If we get into a situation where we are telling each other's parties who they should nominate for positions that becomes very unsafe, because we will obviously have an indication around Sinn Fein as to who they nominate". That gesture will fuel the theory that Sinn Féin will seek to hinder and sabotage these negotiations, due to a lack of genuine will to make them work, however, the party's characterisation of the secretary of state does have a certain ring of familiarity about it.
"Without fundamental change on their part there can not be the type of progress that people want".
She added: "People want equality for all, they want respect in the institutions, for republicanism".
Sinn Fein has publicly stated on several occasions that the party will not support the Democratic Unionist Party leader as first minister until her role in the Renewable Heat Incentive (RHI) scandal has been clarified by an inquiry.
There were lots of cheers for the embattled Mrs Foster from her MLAs, which suggests that for the meantime at least she has managed to avoid any challenge to her leadership.
Mrs Foster set up the botched energy scheme, which could cost the Northern Ireland tax payer £490 million.
Arlene Foster has warned Sinn Fein it is "dangerous" to dictate to other parties who they should nominate for government positions.