Your mistake is thinking that quick can only do the job of an adjective. In fact, the word quick can function as a noun, an adjective, or an adverb in English. The OED says of it the following, with selected citations:
C. adv. 1. a. = quickly. This use is now usually avoided in educated speech and writing, though found in some standard colloq. constructions.
- 1788 Charlotte Smith Emmeline (1816) IV. 55, ― I am going··to Havre, whence I shall get the quickest to Southampton.
- 1840 Dickens Barn. Rudge x, ― The person who’d go quickest, is a sort of natural.
- 1865 Tennyson *On a Mourne*r iii, ― Nature··on thy heart a finger lays, Saying ‘Beat quicker’.
- 1874 Green Short Hist. ii. 88 ― A peaceful invasion··followed quick on the conquest of the Norman soldiery.
- 1936 C. Sandburg People, Yes 83 ― Some men dress quick, others take as much time as a woman.
- 1968 Listener 11 July 38/3 ― I’ve never known a journey go so quick.
- 1979 Times 23 Nov. 5/4 ― The brash and selfish values of a ‘get rich quick’ society.
There is also this adverbial use:
2. Used imperatively. (In some cases perh. representing the adj. in the phr. be quick!) See also quick march 2.
- 1596 Shaks. Merch. V. ii. ix. 1 ― Quick, quick I pray thee, draw the curtain strait.
- 1604 Shaks. Oth. V. i. 3 ― Quicke, quicke, feare nothing; Ile be at thy Elbow.
- 1822 Shelley tr. Calderon iii. 176 ― Livia, quick, bring my cloak.
- 1852 Mrs. Stowe Uncle Tom’s C. v. 31 ― Get on your clothes, old man, quick!
- 1872 Tennyson Gareth & Lynette 147 ― Nay-quick! the proof to prove me.
There are lots of seeming-adjectives that can be used adverbially. For example, you can have fast women who run fast.
You should probably read this answer on the nature of adverbial constructions.