I recently got a paper published and reported a result in the body of the text that is right. However, this value is based on values in the supplementary material that are extremely close to the right values but with a difference (error, let's be honest) in the last decimal place. For example, the right would be "2,765 and 2,777" and I reported "2,764 and 2,778". The main value that results from them and that is disclosed in the paper, is right. That wrong approximation of the mentioned values do not change the conclusions at all and my advisor told me to move on and forget it, that a corrigendum would not be necessary since the mistake is minor and it could potentially damage my career. What is your advice?
How good is your accuracy? For example, if you are measuring the fine structure constant whose current accepted value is ~7.2973525693(11) x 10^(-3), then an error in the fourth decimal place matters. You'd be claiming a reasonably large deviation from the accepted value.
On the other hand, if you are measuring the parallax to Alpha Centauri, whose current accepted value is 750.81 ± 0.38 mas, then an error in the fourth decimal place simply does not matter (and you should not report it in the first place).
And if you are doing something like "express 1/13 in decimals" and write 0.07693 instead of 0.07692, it's not something to worry about - in fact if someone attempts to duplicate your results, there's a good chance they get something similar but not exactly the same, simply because of rounding errors. Perhaps they rounded an earlier result and you didn't, for example. It only starts to matter when the precision is good enough that the difference should not be there.
Your advisor is probably giving good advice. They know the field and whether such "small" deviations are significant in practice or not. In some fields they might be, of course, but unlikely in most fields for most purposes.
The question is whether bad things could happen if someone relies on the slightly incorrect values. In nuclear energy the difference between "not critical mass" and "critical mass" is small. But such is unlikely for most purposes.
I agree with other answers that this seems too minor to issue a corrigendum for. You may consider fixing the error in a preprint version though. That said, you mention that the wrong value is listed in supplementary material. I've previously been told by one publisher (APS) that they allow for (at least minor) updates to such supplemental material at any time. I do not know how widespread this practice is, but if your publisher has a similar policy it may thus be possible to correct the values without needing to issue a corrigendum.