He who will not learn when he is young will regret it when he is old.

少壮不努力，老大徒伤悲。

It is much to be regretted that you can’t join us in the trip.

你不能和我们一道去旅行，真是遗憾。

I have no regrets about leaving.

我毫不后悔离开。

Much to my regret, I am unable to accept your kind invitation.

非常遗憾，我不能接受你的盛情邀请。

It is with great / deep regret that I accept your resignation.

接受你的辞呈，我感到非常遗憾。