User blog comment:Deadpool(Earth 616)/No Spider-Sense in The Amazing Spider-Man?!!/@comment-4276072-20120730180219/@comment-4652104-20120804085703

Spider sense has a limited range/effect. Spidey can sense danger, objects approaching him and suchlike. He cannot however detect cabs in neighboring streets or lizards in adjacent tunnels. The web allowed him to cover a much grater area of the sewers. Plus, I would venture that the ability to discern whether it was the Lizard or some random rat nudging the web, may have something to do with spider sense.