The singer was targeted with a string of online messages after she appeared to show support for the No campaign. The former Eurythmics star, 59, took a picture of a Union flag on display in a shop window in London.
She posted it on her Facebook page and said: "Out and about in London Town.. something almost quaintly old fashioned about this Union Jack in a shop window. It seems to have lost some of the connotations that made me feel uncomfortable back in the day."
The post sparked a heated debate on the Sweet Dreams singer's website, with some accusing her of sending a subliminal message that she wanted Scots to vote no.
Lawrence Target wrote: "Don't you dare come out against our independence. Inform yourself, for this is a new and beautiful horizon for Scotland and a better future for our children."
Lennox later attempted to calm tempers by saying: "Folks, just a mention, I can't vote on the issue of Scottish independence as I don't live in Scotland. The people who reside there will decide for themselves what they want to do.
"My flag post yesterday had no hidden message or agenda."
However, her comments led to calls for her to avoid posting similar images in case it influenced her fans. Lenny Lane wrote: "I understand your position Annie. However, like it or not, you are viewed as an ambassador for all good things Scottish. You're a smart and respected lady. Perhaps some discretion is needed."