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1.
The regretful feeling of putting too many photos/an embarrassing photo on Instagram the morning after a big night.
"I instagret that photo I put up of me naked rolling around in my grandfathers ashes."

"Her box gap is smaller than it used to be, she'll be instagretting that photo this morning!"
by Be Ess March 16, 2013
 
2.
A combination of the words "instant" and "regret;" the instant regret you feel after doing something incredible stupid and rash.
Lindsay was filled with instagret after telling her boyfriend that she still sleeps with a nightlight.
by lindyjamz June 21, 2011