We propose a method to perform audio event detection under the common constraint that only limited training data are available. In training a deep learning system to perform audio event detection, two practical problems arise. Firstly, most datasets are "weakly labelled" having only a list of events present in each recording without any temporal information for training. Secondly, deep neural networks need a very large amount of labelled training data to achieve good quality performance, yet in practice it is difficult to collect enough samples for most classes of interest. In this paper, we propose a data-efficient training of a stacked convolutional and recurrent neural network. This neural network is trained in a multi instance learning setting for which we introduce a new loss function that leads to improved training compared to the usual approaches for weakly supervised learning. We successfully test our approach on two low-resource datasets that lack temporal labels.