遗憾是一种惋惜，通常是说你应该做到，想要做到或可以做到却没有做到，它是一种表示遗憾，无法控制或者补救。而对不起指表示抱歉的口头语，有本质的区别

The 'sorry' in English is equivalent to "对不起" and “遗憾” in Chinese. Say your dad just passed away, then I say "I'm sorry." That's 遗憾。 Say I did something wrong, I might say "I'm sorry." That's 对不起。

对不起 is a frequently-used phrase to express "sorry" 遗憾 is like "a pity, a shame, unfortunately " in English and it is quite formal. 很遗憾，这次法国足球队没有进入世界杯。

"对不起"means that you did something wrong to others and have to apology. And 遗憾 means that you want do something again and hope a better results.

Thanks so much