My textbook states, that the DDH-assumption is not satisfied when we use the group $\mathbb{Z}/p \mathbb{Z}$ and demonstrates an attack using Eulers Criterion. After that, it states that one should use the group of quadratic residues ($\operatorname{QR}$) over $\mathbb{Z}/p \mathbb{Z}$, where $p=2q+1$ is a safe prime.
I had a look at the El Gamal encryption scheme (which uses the DDH-assumption) and saw, that the message that we want to encrypt has to lie in the group that we choose. If this group is $\mathbb{Z}/p \mathbb{Z} = \{1,2,3,\ldots ,p-1\}$ we can encrypt every message, that is not greater than $p-1$. However, if we use the group of $\operatorname{QR}$'s over $\mathbb{Z}/p \mathbb{Z}$, I think that some messages (namely $(p-1)/2$ many) cannot be encrypted.
If this is true, how would one solve this in practice?