At our current understanding of consciousness we have no way of observing its presence or absence except subjectively. So at this point there is no scientific way of either proving or disproving that a carrot have consciousness.
You may think it is "obvious" that a carrot does not have consciousness. Which is fine, but that doesn't make the opinion science. For what it is is worth I intuitively think consciousness requires a complex brain, but I recognize I cannot prove or disprove it given our current understanding.