Gotinhas is the diminutive form of gotas, meaning "drops". The use of the diminutive adds a tender and delicate nuance, implying "little drops" or "tiny drops".
In the context of the song, it refers to the small tears that will fall from the singer's eyes, and also to the tears that will wet the face of the person leaving. This word evokes a sense of fragility and sadness, making it particularly poignant and memorable in this farewell song.