Translation:My watch works, but not accurately.
Something that is precise makes very fine measurements. If you have a watch that measures time down to the millisecond, it is very precise, even if the time is wrong. One the other hand, you might have a watch that does not even have a minute hand, but which shows the hour accurately at all times. It is accurate, but not precise, while the earlier watch was precise, but not accurate. It is a bit like the distinction between being logical and being correct.
Yet, there is a word for accuracy: akurateco.
http://reta-vortaro.de/revo/ When you look up precise, you see two words "precize" and "akurata" with the number 2 for its second meaning.