気分を害したらごめんねって英語でなんて言うの？

If the offending statement has not yet been said but you are about to say it, it is appropriate to apologize beforehand. This reduces the effect that the offending statement may have on the other person. Since you have apologized in advance, the other person may not be as annoyed with you as he/she would have been had you not apologized in advance.
So, you may say:
I am sorry if I may offend you by what I am about to say.

I know this isn't what you want to hear but...
Don't take this personally...
I don't want to hurt your feelings...

You can also say
I don't know how to say this, I don't want to offend you but...
I hope this doesn't upset you but...
This might offend you but I need to say it...
Don't be offended but...
*Please don't be upset or offended but...

Hope this helps! ^ ^

It is very wise to caution someone you are speaking to that a statement may be offensive. It shows that your intent is not to offend, but to simply share your point of view. Americans are very sensitive to tone. Often times, it is not what you say, it is how you say it. The second sentence example should really only be used among your friends. It is very informal although you will hear it very often. It can come across unapologetic.

▪ I am sorry if I'm about to offend you but...
▪ Sorry if I am going to sound rude but...
▪ Don't be offended but...

>Any of the above can be used.
>All the sentences are polite by first apologizing before saying something that can be rude or offensive.

Open by giving the apology (sorry, apologise), and then follow this with a word (offends, upsets) that describes that what you say may cause them to have some feeling of negativity.

The apology keeps it polite (sorry, apologise), so that when you give them the warning word (offend, upset) they will know that your intentions are good and you don't mean to cause any bad feeling.

Either of the above would be a good way of explaining you don't want to offend someone with what you are going to say.