Jessie Armstead and Lawrence Taylor, Harry Carson and Carl Banks — Jonathan Casillas named them all as he stood by his locker Thursday. All those men, he said, represented an organizational pride in the Giants’ defense. One, he said, that he’s gunning to get back.

“Having those guys reminds you of the importance of being great defenders and being the New York defense and [to] represent [the team],” the Giants linebacker said, in that moment specifically referring to Armstead and Banks, who often are around the team in their capacity as coach (Armstead) and analyst (Banks). “All those guys, those are defensive guys who took this team into the playoffs . . . In order for us to have success as a team, we have to be better defensively.”

It shouldn’t be too hard. The Giants were the worst defense in the league last season, allowing an NFL-high 6,725 yards, but made significant moves in the offseason in hopes of being the kind of defense they used to be.

Now, with Casillas as one of the three captains this season — Eli Manning and Zak DeOssie are the others — the Giants hope his leadership skills will help solidify a unit peppered with new and young players. Though he’s been battling a rib injury, he fully expects to be able to play Sunday, he said.

“I’ve been getting the El Capitan jokes,” said Casillas, 29. “The biggest thing for me is when I hear from a guy like a DRC [Dominique Rodgers-Cromartie] and a Leon Hall, guys who have played longer than me in the league, saying, ‘I’m glad my vote didn’t go to waste and it’s well-deserved.’ That means so much to me.”

In addition to the team-chosen season captains, Ben McAdoo said he’ll name game-day captains. This week against the Dallas Cowboys, those honors go to Jason Pierre-Paul, Mark Herz lich and Rashad Jennings.

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“I’m excited for those guys,” McAdoo said of Casillas, Manning and DeOssie. “They’ve earned it and they’ve been working hard all camp and it’s a great opportunity for them to lead.”

Casillas — something of a surprise pick — has been “very motivated to perform at a high level,” McAdoo said. “He’s been very nosy around the football, finds the ball well and takes advantage of his opportunities when he gets his hands on the ball. He’s a guy that communicates well and the guys respond to him.”

That’s a trait Casillas takes some measure of pride in. “It was actually one of my goals for this year” to become a captain, he said. “I’m always talking to the younger guys and guys who don’t know exactly what it is to be a pro. You’ve got to learn to do it. You just don’t come into this game and be a pro. You have to learn to do it. It’s an acquired skill.

“It’s surreal. Being a hometown guy [from New Brunswick, New Jersey] . . . being the captain of a Jersey team . . . It’s something you could dream of as a kid.”

Notes & quotes: McAdoo said all but defensive tackle Robert Thomas (illness) are likely to be available Sunday. That includes wide receiver Dwayne Harris, who left practice Thursday with heat exhaustion.