Super-resolution ultrasound (SR-US) imaging shows great promise as a clinical technique that can improve ultrasound (US) resolution by an order of magnitude. Current algorithms for SR-US suffer from high complexity and long computation times, precluding real-time imaging. Neural networks can be viewed as general function approximators and can process images at frame rates suitable for a real-time application. The goal of this study was to evaluate the effectiveness of deep networks to learn algorithms for tissue signal suppression while improving performance of SR-US for visualization of microvascular networks. In this study, deep 3D convolutional neural networks (3DCNNs) were chosen to perform spatiotemporal filtering to suppress the tissue signal and perform microbubble (MB) segmentation in place of conventional signal processing methods, e.g. singular value decomposition (SVD), singular value filtering (SVF), or difference filtering (DIF). For each method, a 3DCNN was trained with the respective conventional signal processing algorithm as ground truth. Three 3DCNN architectures with 6 to 7 layers and an input size of 9 x 9 x 9 pixels were evaluated. In vivo data was collected from a cancer-bearing murine model and images were captured with a clinical US scanner equipped with a 15L8 linear array transducer. In vivo data were used to train the networks and testing was based on an in vivo dataset not used in training. The deep networks reached testing accuracies of 97.1% for the DIF implementation with promising performance improvements. The average processing frame rate for in vivo images was 50 Hz with graphical processing unit (GPU) acceleration. Deep learning shows potential for effective spatiotemporal filtering, improving performance of SRUS towards a real-time imaging modality.