[I]n English /t, d, n, l/ are retracted before /r/. [emphasis added]
English Language & Usage Stack Exchange is a question and answer site for linguists, etymologists, and serious English language enthusiasts. It only takes a minute to sign up.Sign up to join this community
'Retracted' basically means that those consonants are articulated farther back in the mouth, and sometimes referred to as 'backed'. The opposite is 'advanced'.
In the examples you give, try saying dog and drink while concentrating on the position of the tip of your tongue. In dog, it should be on the ridge (the alveolar ridge) behind your top teeth, while for drink it goes further back, ready to articulate the /r/.
For a comparison, you could try cork, in which the first /k/ is backed and the final one isn't, and then keen in which the /k/ is advanced.
If you have trouble feeling the difference, some recommend sticking your fingers in your mouth as you say the word. Personally, I wouldn't recommend it.