Face recognition systems are widely deployed in high-security applications such as for biometric verification at border controls. Despite their high accuracy on pristine data, it is well-known that digital manipulations, such as face morphing, pose a security threat to face recognition systems. Malicious actors can exploit the facilities offered by the identity document issuance process to obtain identity documents containing morphed images. Thus, subjects who contributed to the creation of the morphed image can with high probability use the identity document to bypass automated face recognition systems. In recent years, no-reference (i.e., single image) and differential morphing attack detectors have been proposed to tackle this risk. These systems are typically evaluated in isolation from the face recognition system that they have to operate jointly with and do not consider the face recognition process. Contrary to most existing works, we present a novel method for adapting deep learning-based face recognition systems to be more robust against face morphing attacks. To this end, we introduce TetraLoss, a novel loss function that learns to separate morphed face images from its contributing subjects in the embedding space while still preserving high biometric verification performance. In a comprehensive evaluation, we show that the proposed method can significantly enhance the original system while also significantly outperforming other tested baseline methods.