Word for something I should have said

Solution 1:

Based on your comment:

where I wish I would have explained something about myself with a story, but I didn't think to do it at the time

For that specific situation, one might call it an Afterthought

An idea, response, or explanation that occurs to one after an event or decision

In addition, I think a good general phrase for that would be Missed Opportunity. Where you had a chance to add additional information but either forgot, or it didn't come up naturally in conversation.

Solution 2:

In English, we use a French idiom esprit de l'escalier to refer to a witty retort that we could have made during an argument, but which only comes to us (often shortly) after the opportunity has passed.

Here's the definition from Oxford Dictionaries Online:

esprit de l'escalier

NOUN

mass noun

Used to refer to the fact that a witty remark or retort often comes to mind after the opportunity to make it has passed.

Example sentences

‘I am frequently afflicted with esprit de l'escalier.’

‘Now if I'd managed to say all that off the cuff then I would be a genius comedian, but as it was I had to make do with experiencing esprit de l'escalier on the way home.’

Solution 3:

A comeback is a retort made at the time.

An afterwit is the delayed kind of comeback which is only thought of after the event.

Afterwit : A good comeback, retort one thinks of only after the end of discussion or after leaving a social gathering.

Wiktionary

There is also the term staircase wit which refers to the comment made by Denis Diderot (Wikipedia) after he was lost for words and only thought of a retort when he was 'at the bottom of the stairs'.

Solution 4:

Not quite that exact meaning of specifically not having said something, but the phrases in hindsight or in retrospect spring to mind, i.e:

In hindsight, I should have mentioned I have a PhD.
In retrospect, I don't think boasting about my 'days without showering' record was such a good idea.

A relevant phrase is also "with the benefit of hindsight" which can be used similarly:

With the benefit of hindsight, I can now say that flirting with the interviewer was a bad idea.

_{Note. There is no equivalent "benefit of retrospection" phrase as far as I'm aware.}

Dictionary links

https://www.vocabulary.com/dictionary/hindsight
https://www.vocabulary.com/dictionary/retrospection

There's also a related concept called the hindsight bias (or as per the witty quote: "Hindsight is always twenty-twenty") --- this is when one judges in hindsight the outcome of a decision as being more predictable than it actually was when the decision was made.

Solution 5:

Your comment about the job interview suggests that perhaps this isn't the tone you want, but a joke term usually associated with the sense of missed witty retorts and comebacks is "afterism", modelled on "aphorism".

aphorism, n.: A concise, clever statement.

afterism, n.: A concise, clever statement you don't think of until too late.

At least one reference attributes this quote to American author James Alexander Thom.