Robot perception systems need to perform reliable image segmentation in real-time on noisy, raw perception data. State-of-the-art segmentation approaches use large CNN models and carefully constructed datasets; however, these models focus on accuracy at the cost of real-time inference. Furthermore, the standard semantic segmentation datasets are not large enough for training CNNs without augmentation and are not representative of noisy, uncurated robot perception data. We propose improving the performance of real-time segmentation frameworks on robot perception data by transferring features learned from synthetic segmentation data. We show that pretraining real-time segmentation architectures with synthetic segmentation data instead of ImageNet improves fine-tuning performance by reducing the bias learned in pretraining and closing the \textit{transfer gap} as a result. Our experiments show that our real-time robot perception models pretrained on synthetic data outperform those pretrained on ImageNet for every scale of fine-tuning data examined. Moreover, the degree to which synthetic pretraining outperforms ImageNet pretraining increases as the availability of robot data decreases, making our approach attractive for robotics domains where dataset collection is hard and/or expensive.