No biggie. It'll just expel any excess at running temp. As the coolant gets heated, it expands and has to go somewhere. The reservoir was there to catch the overflow and return it to the system as it cooled. Now, instead of the reservoir, it just vents to the ground and sucks air back into the radiator as it cools. It's not a big deal. Once the engine gets up to operating temp, the air is expelled instead of excess coolant.
tl;dr It's fine. It'll stop dripping coolant after a ride or two.