Some online critics suggested it wasn't an error - that the network was trying to make Trump look better by not showing him wearing a baseball cap - considered a breach of protocol - during one of the most solemn duties of a commander in chief.
The return of the bodies of six soldiers killed in a drone attack in Kuwait took place on Saturday at Dover Air Force Base.
But Fox News said archival footage of Trump at an earlier ceremony was inadvertently pulled up by a staff member and used on two Sunday morning telecasts. A spokeswoman noted the correct footage was used at other times, including on Saturday.
"We regret the error and apologise for the incorrect footage," Fox said in a statement.
Fox News anchor Griff Jenkins issued an on-the-air correction on Sunday, saying "we extend our respect and condolences" to the families of the service members killed.
The apology didn't sit well with some critics.
"If any other network did this it would be a huge scandal, Fox would lead the chorus of criticisms and faux-outrage, and people would lose their jobs," said Mehdi Hasan, founder of the online site Zeteo.
Johnny "Joey" Jones, a veteran and co-host of The Big Weekend Show on Fox News Channel, said on social media that he was "embarrassed and ashamed" that this happened.
"My belief was that this was an honest mistake, but that doesn't make it an acceptable one," Jones wrote.
"Few things are more sacred than our heroes who give their lives in the line of duty."
