Entertainment was in short supply as both sides struggled to create chances and defences held firm.
Yeovil had their best opportunity on the hour mark when Ryan Dickson's cross eluded all in the box, before substitute Jabo Ibehre headed just wide for the visitors.
Yeovil remain 11 points clear of the League Two relegation zone in 20th, while Carlisle climb a place to 10th.
Carlisle recorded their fourth straight draw in a drab game at Huish Park.