Initially, logic is not the route to go and will only make the F more emotional (and very mad at you). The best advice I have for Ts is that though it may seem that no progress is being made, you actually are helping an F by allowing them to vent without tell them to calm down, chill out or that they're over reacting. Fs will let go much quicker if they feel heard or at least not further provoked. They also can only take honesty in little sugar-coated bits.
During that initial stage, just try not to do any further (perceived) damage. Reasoning will not help. If it bugs you too much to see tears, explain that you don't want to do any damage and go away temporarily. If the offense was unintentional, explain that.
Usually if the F is way overreacting, they'll soon realize it on their own. If they are just reacting in a way you are unused to reacting yourself, be as nice to them as possible and they'll come around if they feel you care about them. This is the stage where you can discuss it using some logic and they'll be more receptive as long as you don't treat them like they were an unreasonable, overwrought child. (Then they'll want to tell you more about it, with more tears)
Tears are a release and though many Ts feel an allergic reaction to them, for an F they can be therapeutic and wash away feelings of resentment that otherwise would become a big problem between you.