"You shouldn't have!"

"You shouldn't have!"
 

In English, we commonly just say the helping verb "have" without the second verb. For example:
"I bought you a present" -> "You shouldn't have!" (bought one)
"I paid the utility bill" -> "You better have" (paid it)
"Did you see that?" -> "How could I not have?" (seen it)

Does Spanish also just use the helping verb by itself, or is there some other construction?

You cannot use the helping verb like that in Spanish.
You could include the main verb in your answer, but there are better alternatives.

No tenías que haberlo hecho.
No deberías haberte molestado.
"Por qué te has molestado?
No hacía falta.
Gracias (por haberlo hecho).

Buena cosa (que lo hicieras). (you better have)

Claro que sí. (How could I not have?)


There are several other choices.