…てすみませんでした
You use the te-form of a verb to describe the things you have done that you want to apologize for.
Eｘ: デートのやくそくをわすれて、ごめん。(Sorry that I stood you up)
Use …なくてto apologize for something that you failed to do.
Ex: しゅくだいをもっていなくて、すみませんでした。(I am sorry for not bringing in the work.)