First Minister Nicola Sturgeon says Europe should “keep a light on” as Scotland will be “back soon”.
The Brexit transition period formally ended at 11pm on December 31.
Scotland’s trading and travel relationships with EU countries will now be governed by the agreement announced by the UK Government on Christmas Eve.
Sturgeon reiterated the Scottish National Party’s call for an independent Scotland to join the EU.
Scotland’s Constitution Secretary Mike Russell also said the separate Brexit arrangements for Northern Ireland and Gibraltar show independence is the “only alternative”, as the transition period ended.
He was reacting to news that a draft agreement had been reached between the UK and Spain to keep the border with the Rock open on January 1 and beyond.
While Scotland has the same trade arrangements with the EU as England and Wales, there is a separate Northern Ireland Protocol to avoid a hard border with the Republic.
Additionally, on December 31 it was announced that Gibraltar would be covered by a separate treaty.
The Scottish Parliament earlier refused to give legislative consent for Prime Minister Boris Johnson’s Brexit agreement.
Members voted 92 to 30 to say the deal would “cause severe damage to Scotland’s environmental, economic and social interests”, following a debate on Wednesday.
However, Conservatives accused the SNP of hypocrisy for refusing to back the Prime Minister’s deal when it had opposed a no-deal Brexit.
Scottish Conservative leader Douglas Ross said he had written to civil service chiefs seeking an apology for the “bad deal for Scotland” video shared on social media.
Mr Ross said: “This video is a work of shameless propaganda and it’s incredible that a politically neutral civil service would think it is in any way appropriate.
He said Scottish business groups had welcomed the trade deal between the UK and the EU.
Demonstrators gathered outside Holyrood on Thursday afternoon to protest against the end of the transition period.
Morag Williamson, from the group, said: “We are very sad and very angry at the same time.
“We don’t want to leave the family of Europe – but we are being dragged out against our will.”