This paper proposes a method for recognizing audio events in urban environments that combines handcrafted audio features with a deep learning architectural scheme (Convolutional Neural Networks, CNNs), which has been trained to distinguish between different audio context classes. The core idea is to use the CNNs as a method to extract context-aware deep audio features that can offer supplementary feature representations to any soundscape analysis classification task. Towards this end, the CNN is trained on a database of audio samples which are annotated in terms of their respective "scene" (e.g. train, street, park), and then it is combined with handcrafted audio features in an early fusion approach, in order to recognize the audio event of an unknown audio recording. Detailed experimentation proves that the proposed context-aware deep learning scheme, when combined with the typical handcrafted features, leads to a significant performance boosting in terms of classification accuracy. The main contribution of this work is the demonstration that transferring audio contextual knowledge using CNNs as feature extractors can significantly improve the performance of the audio classifier, without need for CNN training (a rather demanding process that requires huge datasets and complex data augmentation procedures).