It turns out that that's not exactly true. Organisms can inherit an acquired trait because not all inheritance is dependent upon DNA. Welcome to "epigenetics:"
A certain laboratory strain of the fruit fly Drosophila melanogaster has white eyes. If the surrounding temperature of the embryos, which are normally nurtured at 25 degrees Celsius, is briefly raised to 37 degrees Celsius, the flies later hatch with red eyes. If these flies are again crossed, the following generations are partly red-eyed – without further temperature treatment – even though only white-eyed flies are expected according to the rules of genetics...
Environmental factors, which change the characteristics of an individual and are then passed on to its offspring, do not really fit into Darwin’s theory of evolution. According to his theory, evolution is the result of the population and not the single individual. “Passing on the gained characteristics fits more to Lamarck’s theory of evolution”, says Paro.
However, he still does not believe Darwin’s theory of evolution is put into question by the evidence of epigenetics research. “Darwin was 100 percent right”, Paro emphasises. For him, epigenetics complement Darwin’s theory. In his view, new characteristics are generated and passed on via epigenetics, subject to the same mechanisms of evolution as those with a purely genetic origin.