That's not right. Deterrence establishes a causal link between the punished and the criminals of tomorrow, who consider the likely outcome of their crime before committing it.

Punishments have a side effect of deterring. People don't wish to be punished so they don't transgress. It shouldn't be the focus of punishment. One problem is that the severity of punishment can be varied in order to vary the deterrent effect, whereas the punishment should fit the crime. That a certain fair punishment is not sufficiently deterring others is immaterial to a given defendant.

Fair punishments may deter insufficiently. The deterrent effect involves the probability of being caught and convicted. A law enforcement and criminal justice system that is not effective at catching and convicting can just crank up penalties to keep the deterrent effect high.