No, a piece of sanitized foil is fine.
You use an airlock with beer becaue you want to let CO2 pressure out, but no oxygen in. You actually want oxygen in your starter, because the point of the starter is the growth phase (which requires oxygen).
This is why people use stir plates and such with starters, but never with beer - the stir plate mixes more oxygen into solution, which promotes more yeast growth.