In the words of OSS legendary instructor, William E. Fairbairn, "In close-quarters fighting there is no more deadly weapon than the knife. An entirely unarmed man has no certain defense against it, and further, the mere sudden flashing of the knife is recently enough to strike fear into your opponent, causing him to lose confidence and surrender."
Dealing with a knife attack is supremely difficult. There is a human tendency to fixate on the
knife hand, but that will only prolong the inevitable. A person with a knife can easily switch grips, switch hands, and just alternate high and low stabs to achieve their aim. The only way to contend with such an attack is to become the attacker: impart a serious injury to the person with the knife and then proceed to impart serial injury until you are confident you can turn your back on the problem.
Easier said than done. To get there takes mental preparation at a minimum (can you really put your finger in someone's eye?) and physical preparation through slow practice to ingrain the ability to exploit an opening and get an injury. The person with the knife must be within arm's length to get you. Therefore, you are already close enough to attack a vital target like the eyes, neck. Whichever target you choose however, you have to put complete effort into it. Envision going through your target to a point three feet behind it.