The expressions "get used to" and "get accustomed to" are followed by the "-ing" form of the verb if you are going to use a verb. It's also correct to use a noun, a noun phrase, a pronoun or a noun clause. Since the "-ing" is the noun form of the verb, or the gerund, it is logical to use this form.
"Used" and "accustomed" are past participles followed by a preposition, in this case "to." Prepositions are followed by a noun, a noun phrase, a pronoun, a noun clause, or a noun form of the verb – that is, the "ing" form.
Here are some examples from the Collins COBUILD* online:
..... so that your child can get used to them
in familiar surroundings
.....I thought I'd never get used to being
in an office all day.
... After a while, you'll get used to the separation
and accept it.
...men and women around the world get accustomed to being
... and I need time to get accustomed to the routine
...get to know each other and to get accustomed to talking
to each other. And ...