Yes and no. Your teacher is right that, in general, you need to use an adverb (usually ending in 'ly') to modify a verb. However, there are some cases where the adjective form is acceptable, and I think that 'quick as you can' is one of these cases. You can even justify it by calling it a 'flat adverb', which has an adjectival form but the function of an adverb. One of the great myths about English is the assumption that the American tendency to use adjective forms rather than adverbs is a sloppy degeneration of the language. This isn't the case at all. In fact, until around the 18th century, adjectives could modify both nouns and verbs - the 'ly' form was a relatively late invention. Phrases such as 'quick as you can' and 'hold tight' are hangovers from that earlier time.

I think your teacher is right, because you want to describe verb and need to use adverb