家に忘れてきたって英語でなんて言うの？

>I forgot my phone at home.
Simple way of saying that you forgot it and you know that you definitely did forget it.
>I think I left my phone at home.
This is when you not sure if you forgot it or lost it.
>I do not have my phone with me, I forgot it at home.

Example
Her: Hey where is your phone?
Me:I do not have my phone with me, I forgot it at home.

You can use any of the above expressions:-

Example:
A : "Where are your office Keys?"
B: "Oops! I forgot them at home.

OR
B: "I left them at home."

"I forgot my iPhone at home."
"I left my iPhone at home when I went to school."

A) I forgot my ... at home!
Forgot-fail to remember.
Example-"he had forgotten his lines"
My-belonging to or associated with the speaker.
Example-"my name is John

B)Oh no! I forgot the .. at home!
*Oh no! - An exclamation or expression of alarm, concern, or resentment about a problem or error.
Example-Oh, no! The rug is on fire!

I hope this helps :-)

The word "accidentally" implies that a mistake was made and that there were no bad intentions in your actions. The word 'oops' is a commonly used interjection that shows that a person has made a mistake.
For example: "Oops! I left my cellphone in the car"

I left it at home is probably the most common and natural way to say this.
Left is the past tense of leave.
Example:
A: Can I use your phone to call my mum?
B: Sorry, I left it at home today.

You want to express that you forgot something at home. There are a couple of examples above. It would be normal to include an explanation as in the second example.

Mistakes do happen, use the sentences above if you forgot something at home.

Unintentional: something that happens by mistake, it was not planned.
Mistakenly: this points to something that is a mistake.

"Sorry, I totally forgot to bring the letter, it was unintentional. I will bring it tomorrow, it is at home in my room."