Creating 3D semantic reconstructions of environments is fundamental to many applications, especially when related to autonomous agent operation (e.g. goal-oriented navigation and object interaction and manipulation). Commonly, 3D semantic reconstruction systems capture the entire scene in the same level of detail. However, certain tasks (e.g., object interaction) require a fine-grained and high-resolution map, particularly if the objects to interact are of small size or intricate geometry. In recent practice, this leads to the entire map being in the same high-quality resolution, which results in increased computational and storage costs. To address this challenge we propose MAP-ADAPT, a real-time method for quality-adaptive semantic 3D reconstruction using RGBD frames. MAP-ADAPT is the first adaptive semantic 3D mapping algorithm that, unlike prior work, generates directly a single map with regions of different quality based on both the semantic information and the geometric complexity of the scene. Leveraging a semantic SLAM pipeline for pose and semantic estimation, we achieve comparable or superior results to state-of-the-art methods on a synthetic and a real-world dataset, while significantly reducing storage and computation requirements.