I'm actually prone to agreeing with you- I think that, ultimately, we have significant capacity for comprehending the mental states and emotions of other terrestrial creatures. Wittgenstein's quote is, however, one of those ideas that does need to be confronted in related discussions.
I'm not familiar with whether Wittgenstein owned pets himself, but his comments were to a great extent representative of the general views of his time on animals. They were often thought of as mere automatons, simply reacting to stimuli, without any real emotions. It was even widely believed that they couldn't feel pain. He's actually rather enlightened in that context- he did seem to believe that they were actually capable of perception and more than merely reacting to stimuli.