The New York City bomber allegedly went on Facebook just before setting off a homemade device and told President Trump he'd failed to protect the U.S.A.

According to the federal criminal complaint filed Tuesday against Akayed Ullah, the bomber took to the social media site with his message to the Prez while on the way to the Port Authority subway before the explosion. 

Per the docs, obtained by TMZ, Ullah allegedly wrote ... "Trump you failed to protect your nation" ... which prosecutors say he posted Monday morning before the incident. They go on to say the message was written with ISIS in mind. 

During a presser about the attack, US Attorney Joon Kim also revealed a search of Ullah's apartment uncovered a handwritten note that read, "Oh America Die In Your Rage."

As we reported ... Ullah was captured alive after detonating what many called a pipe bomb strapped to his person. Three other people were injured, leaving one temporarily deaf.

As for Trump ... he released a statement Monday essentially saying his travel ban was necessary to prevent attacks like this. Sounds like he'll have more ammo for that point now.