The LibDem cabinet minister challenged the Nationalists to explain claims that an independent Scotland would gain swift entry to the EU on the same terms as the UK.
Speaking ahead of an appearance before a Holyrood committee by SNP Culture Secretary Fiona Hyslop, Carmichael said: "The Scottish Government could make a significant contribution to the referendum debate by filling in a great deal of missing detail on its plans to take an independent Scotland into Europe. It's clear there are no shortcuts to entry or to preferential terms and conditions and that a growing number of key figures close to the decision-making process are casting doubts on their preferred route into the EU."
He urged the Scottish Government to reveal which EU countries supported its plans for fast-track membership and to set out alternative proposals if accession talks faced delays. He also questioned the claim that an independent Scotland would be able to negotiate the same membership terms as the UK.
A spokesman for Deputy First Minister Nicola Sturgeon said: "The question Alistair Carmichael needs to answer is why he supports a Tory Government that risks dragging Scotland out of the EU. Scotland is in the EU and has been for 40 years - no member state has said it would veto Scotland's continued membership.
"We have put forward a suggested mechanism by which Scotland can make the transition from being in the EU as part of the UK to being part of the EU as an independent country."