不客气有不同的中文意思，所以英文说法也有很多种。对别人表达感谢的回应：you're welcome/don't mention it等；表达不礼貌或粗鲁时：impolite/rude/unkind等。

不客气的英文：
you're welcome
impolite
rude
blunt
don't mention it

参考例句：

He was unkind to you.
他对你不客气。

Do not mention it .
不客气。

Being called by a nickname is not usually uncomplimentary
被人起了绰号并不一定是不客气

Such unkind remark was not called for.
这种不客气的话真不该讲。

The customer was angry with the sales girl for her impolite answer.
那位顾客对女店员不客气的回答感到忿怒。

He addressed me forcibly in the vernacular
他用下流话对我不客气地说话。

Your unkind remark was not called for.
你这种不客气的话真不该讲。

She is rather short with him when he ask for help.
他请她帮帮忙，她却不客气地把他顶了回去。

Don't mention it. You should drink some water and go to lie down.
不客气，你应该多喝些水，去躺一下。

I'll put a flea in his ear if he bothers me once more.
如果他再来打扰的话，我就要对他不客气了。

you是什么意思：
pron. 你，您；你们，您们；各位，大家

welcome是什么意思：
v. 欢迎，款待，愉快的接受，迎接
n. 欢迎，迎接，接受；欢迎辞
adj. 受欢迎的，令人愉悦的，不受限制的
int. 欢迎

Welcome you to the fair.
欢迎您到交易会来。

Whomever you invite will be welcome.
你邀请的任何人都将受欢迎。

A constant guest is never welcome
常客令人厌

impolite是什么意思：
adj. 失礼的，粗鲁的

Don' t be impolite to her !
不要对她没礼貌！

He was scourged for his impoliteness.
他的无礼举止受到了严厉的批评。

It is impolite to poke the top of food with chopsticks.
用筷子戳食物项端是不礼貌的。

（来源：沪江英语）