The hilarious moment went down on ESPN2 as the Giants legend was sharing his experiences going up against the Philadelphia Eagles ... describing their fans as absolutely ruthless.

"You go to Philly, you're getting the double bird right away from a 9-year-old kid," Eli told Peyton and 4th quarter guest Chris Long.

"I would give the bird, I don't know, can we do that?? I'm sure you can blur that out, right??"

As it turns out, E, -- no, you can't do that and no, they couldn't blur it out ... but that didn't stop him from holding up the gesture for a few solid moments.

Despite the hiccup, Eli continued his story like nothing happened ... claiming fans would say things about his mom that he wouldn't say over the air (apparently he limits himself to one FCC violation per game).

"They're saying things about my mom and Peyton, I can't even tell you what they said about my mom," Eli added.

The Manning-cast has been a huge hit through 3 weeks ... with guests like LeBron James, Russell Wilson, Gronk, and Charles Barkley joining the bros to talk football.

Travis Kelce also flirted with more mature content when he was on during Week 1 ... dropping an s-bomb.

No word on if the FCC will hand down any fines, but Eli ended up apologizing for the whole thing.

"Sorry, earlier I gave the double bird. I guess that’s frowned upon, so I apologize if I offended anybody. That’s just what a 9-year-old did to me and I thought I could do it back," Eli said.