In photoacoustic imaging, accurate spectral unmixing is required for revealing functional and molecular information of the tissue using multispectral photoacoustic imaging data. A significant challenge in deep-tissue photoacoustic imaging is the nonlinear dependence of the received photoacoustic signals on the local optical fluence and molecular distribution. To overcome this, we have deployed an end-to-end unsupervised neural network based on autoencoders. The proposed method employs the physical properties as the constraints to the neural network which effectively performs the unmixing and outputs the individual molecular concentration maps without a-priori knowledge of their absorption spectra. The algorithm is tested on a set of simulated multispectral photoacoustic images comprising of oxyhemoglobin, deoxy-hemoglobin and indocyanine green targets embedded inside a tissue mimicking medium. These in silico experiments demonstrated promising photoacoustic spectral unmixing results using a completely unsupervised deep learning approach.