Neurosymbolic (NeSy) AI has emerged as a promising direction to integrate neural and symbolic reasoning. Unfortunately, little effort has been given to developing NeSy systems tailored to sequential/temporal problems. We identify symbolic automata (which combine the power of automata for temporal reasoning with that of propositional logic for static reasoning) as a suitable formalism for expressing knowledge in temporal domains. Focusing on the task of sequence classification and tagging we show that symbolic automata can be integrated with neural-based perception, under probabilistic semantics towards an end-to-end differentiable model. Our proposed hybrid model, termed NeSyA (Neuro Symbolic Automata) is shown to either scale or perform more accurately than previous NeSy systems in a synthetic benchmark and to provide benefits in terms of generalization compared to purely neural systems in a real-world event recognition task. Code is available at: https://github.com/nmanginas/nesya