Whitehall sources said some of the 26 ambassadors, in particular the one from Spain, were unhappy at the presentation.
The Spanish Government is facing pressure from the independence movement in Catalonia.
No-one at the Spanish embassy or consulates in London and Edinburgh could be contacted.
Mr Salmond outlined his "vision of an independent Scotland in Europe" at an event in the Irish Embassy in London.
The Scottish Government said he focused on the Edinburgh Agreement and the transition paper published last week.
A spokesman added: "The First Minister told the ambassadors Scotland has always grasped internationalism because, as a nation, we have been used to sharing sovereignty, in one form or another, for a considerable period of time."
Mr Salmond said this was part of the reason euroscepticism did "not have the same potency in Scotland" and the Scottish Government did not support the policy of an in-out referendum on EU membership.
The First Minister's speech was called a "private event" and it was made clear no direct quotes would be made available.
Margaret Curran, the Shadow Secretary of State for Scotland, said: "We're becoming used to a culture of secrecy from this First Minister.
"First it was the EU legal advice, then he spent taxpayers' money to cover up whether the advice existed and now he's having closed-door meetings with ambassadors.
"What has the First Minister got to hide?