I make my egg pasta with the food processor. Works everytime.
2 cups white flour
3 medium eggs
1 TBS olive oil
ľ tsp salt (optional)
ľ cup extra flour for working the dough.
Put all ingredients into the food processor in the order given and process quickly until a ball forms (about 30 seconds), and it clings away cleanly from the sides of the container.
If it appears too sticky, remove the top and sprinkle one tablespoon of flour. Process briefly until it clings away from the sides. If it appears too dry and does not form a ball, you may need to add a little water, a tablespoon at a time. You should not need more than one or two tablespoons of water, or one or two tablespoons of flour. Wrap in plastic and store in the refrigerator until needed. If you plan to use it right away, let it rest for fifteen minutes covered with a kitchen towel.
Note: Do not knead the pasta, contrary to bread, egg pasta works better if it is a rather stiff mass. It will be easier to handle after the gluten has relaxed. You can freeze unused pasta, it will get slightly darker in color, but nothing to worry about, itís just the oxidation process.
P.S. When you dropped the pasta was the water at a hard boil? For home made egg pasta it is best a gentle boil, and instead of draining it it is safer to scoop it out with a large slotted spoon.