Jean-Claude Juncker, who formally took up his post yesterday, warned that it would be at least five years before the bloc was ready to take on any more members from eastern Europe.
But his remarks - suggesting no further enlargement until 2019 - were seized upon by pro-UK politicians as evidence that an independent Scotland would also be kept out of the EU.
Labour MSP Jackie Baillie, speaking on behalf of Better Together, said: "It is now clear that if we leave the UK, we would be leaving the EU. This would put thousands of Scottish jobs at risk and would be massively damaging to our country."
Scottish Secretary Alistair Carmichael also linked what he called Mr Juncker's "highly significant intervention" with previous warnings from Mr Barroso and Herman Van Rompuy, the president of the EU Council. But Ms Sturgeon, the Deputy First Minister, called on No campaigners to withdraw their remarks after it was later reported that Mr Juncker's spokeswoman said he was not referring to Scotland.
Ms Sturgeon said: "This blatant act of dishonesty is a major blow to the credibility of the No campaign.
"In their desperation to talk Scotland down and spread fears and smears, the No camp have wilfully twisted what Jean-Claude Juncker said. They said that Mr Juncker was talking about Scotland - and his spokeswoman has confirmed that he was not. Their claims now lie in tatters."
Ms Sturgeon said the campaign against independence had distorted remarks made by Mr Juncker and called for them to withdraw their "bogus assertions" immediately and apologise.
"The only threat to Scotland's place in Europe is a Westminster in/out referendum."
Mr Juncker's words were focused on calling a halt to what in recent years has appeared to be a relentless expansion eastwards.
The former Luxembourg premier said: "When it comes to enlargement, I fully recognise that this has been an historic success that brought peace and stability to our continent. However, the union and our citizens now need to digest the addition of 13 member states in the past 10 years.
"The EU needs to take a break from enlargement so that we can consolidate what has been achieved among the 28.
"This is why, under my presidency of the Commission, ongoing negotiations will continue, and notably the Western Balkans will need to keep a European perspective, but no further enlargement will take place over the next five years.
"With countries in our Eastern neighbourhood, such as Moldova or Ukraine, we need to step up close co-operation, association and partnership to further strengthen our economic and political ties."
The EU is deeply concerned by both conflict in Ukraine and the readiness of would-be members such as Serbia, which formally applied to join in January. The last country to sign up to the EU was another former Yugoslav republic, Croatia, a year ago this month.
Michael Keating, director of ESRC Scottish Centre on Constitutional Change, said: "This as about enlargement eastwards and not about Scotland. Juncker was talking about not letting new countries into the EU, not about kicking out countries that are already in.
"Why would Juncker want to have the problem of throwing Scotland out of the single European market, which would be much more complicated than letting a new country in, on top of all his other problems?"
Professor Keating, an international authority on secessionist politics, said Mr Juncker's stance on Scotland was significantly different to that of his predecessor, Jose Manuel Barroso, who early this year said it would be difficult if not impossible for Scotland to remain in the bloc.
Leading SNP figures have already signalled they believe they can work with Mr Juncker, whose appointment was unsuccessfully opposed by Downing Street.