后悔means you blaming yourself for something you have done.If give you a chance,you definitly will start again. 遗憾is different.most of the part is not caused by yourself.It's a sense of loss and longing for someone or something gone,you can do nothing.so you'll not have strong feeling of make up. another expression is:遗憾 is caused by subjective while后悔 is caused by objective. such as:life can have regert, but can't have pity.人生可以有后悔，但不能有遗憾。 this 2 phrases often used to express love. At perfect time, we meet a bad person is 后悔 At wrong time ，we meet a perfect person is 遗憾 in short:后悔:you have done it. 遗憾:you have never done before. My English is poor. i don't know whether I have exactly explain.If you still have questions,I'm glad to help.

遗憾：不称心，惋惜（在外交文件上常用来表示不满和抗议）【usu.used in diplomatic documents to express displeasure and protest】 make a sentence：功亏一篑，令人遗憾。（It's a pity to fall short of a final effort）

区别是什么？ Difference!

与“regret to do” and “reget doing”比较相近。

遗憾 is not as intensive as 后悔， 后悔： something that you can do it (very well) originally, but you don't.So, it suggests that you want to change it if you could. 遗憾： something that you had endeavored but it exceeded your ability much or you didn't take account of it. So, they are similar words. P.S: Please point out mistakes in my sentences, thanks a lot.