Deep learning has helped achieve breakthroughs in a variety of applications; however, the lack of data from faulty states hinders the development of effective and robust diagnostic strategies using deep learning models. This work introduces a transfer learning framework for the autonomous detection, isolation, and quantification of delamination in laminated composites based on scarce low-frequency structural vibration data. Limited response data from an electromechanically coupled simulation model and from experimental testing of laminated composite coupons were encoded into high-resolution time-frequency images using SynchroExtracting Transforms (SETs). The simulated and experimental data were processed through different layers of pretrained deep learning models based on AlexNet, GoogleNet, SqueezeNet, ResNet-18, and VGG-16 to extract low- and high-level autonomous features. The support vector machine (SVM) machine learning algorithm was employed to assess how the identified autonomous features were able to assist in the detection, isolation, and quantification of delamination in laminated composites. The results obtained using these autonomous features were also compared with those obtained using handcrafted statistical features. The obtained results are encouraging and provide a new direction that will allow us to progress in the autonomous damage assessment of laminated composites despite being limited to using raw scarce structural vibration data.