This is not directly available within the $search stage to my knowledge. There’s also the associated feedback engine post for your request which you can vote for in the meantime.
You could possibly perform the $search stage first as per normal followed by a $match stage using the $ne operator (As Nenad has mentioned) if it suits your use case although I do understand that this would not make use of any indexes (for the $match stage that’s after the $search stage).
Regards,
Jason