Neural networks also have "inner eyes". From being able to "dream" images and sequences that haven't appeared in the training data, but look plausible.

Or being able to manipulate learned concepts. Like word2vec turns words into vectors that can be combined in complicated ways. E.g. words for colors will be different based on what the colors are associated with (e.g. red is associated with "danger", or green is associated with "nature", etc.)

Make this process much more complex, and intelligent, and then ask it what it "feels". It will probably give responses very similar to humans. It "feels" complicated internal experiences that it can't completely explain or understand.

It certainly wouldn't feel like it's "just combining stimuli with internal state to get output signals". Being an algorithm doesn't feel like you are an algorithm, from the inside.