不客氣有不同的中文意思，所以英文說法也有很多種。對別人表達感謝的回應：you're welcome/don't mention it等；表達不禮貌或粗魯時：impolite/rude/unkind等。

不客氣的英文：
you're welcome
impolite
rude
blunt
don't mention it

參考例句：

He was unkind to you.
他對你不客氣。

Do not mention it .
不客氣。

Being called by a nickname is not usually uncomplimentary
被人起了綽號并不一定是不客氣

Such unkind remark was not called for.
這種不客氣的話真不該講。

The customer was angry with the sales girl for her impolite answer.
那位顧客對女店員不客氣的回答感到忿怒。

He addressed me forcibly in the vernacular
他用下流話對我不客氣地說話。

Your unkind remark was not called for.
你這種不客氣的話真不該講。

She is rather short with him when he ask for help.
他請她幫幫忙，她卻不客氣地把他頂了回去。

Don't mention it. You should drink some water and go to lie down.
不客氣，你應該多喝些水，去躺一下。

I'll put a flea in his ear if he bothers me once more.
如果他再來打擾的話，我就要對他不客氣了。

you是什么意思：
pron. 你，您；你們，您們；各位，大家

welcome是什么意思：
v. 歡迎，款待，愉快的接受，迎接
n. 歡迎，迎接，接受；歡迎辭
adj. 受歡迎的，令人愉悅的，不受限制的
int. 歡迎

Welcome you to the fair.
歡迎您到交易會來。

Whomever you invite will be welcome.
你邀請的任何人都將受歡迎。

A constant guest is never welcome
常客令人厭

impolite是什么意思：
adj. 失禮的，粗魯的

Don' t be impolite to her !
不要對她沒禮貌！

He was scourged for his impoliteness.
他的無禮舉止受到了嚴厲的批評。

It is impolite to poke the top of food with chopsticks.
用筷子戳食物項端是不禮貌的。

（來源：滬江英語）