In the UK 'blue funk' refers to a state of fear or panic. (In this case 'blue' is used to add emphasis or urgency; this may possibly be related to the use of 'blue' as a slang term for amphetamine).
In the US it refers to depression, dejection or melancholy. (In this case 'blue' refers to a blue mood, as in feelings of sadness).
A couple of dictionaries (target nationality not specified) define it as 'nervous depression,' an interesting compromise betwixt the two.