The Northern Irish actor appears as Tardos Mors in the science fiction epic alongside Rome co-stars Polly Walker and James Purefoy.
Hinds told Digital Spy that Stanton first approached him to star in the movie after seeing him perform in a stage production of Burnt by the Sun.
"Andrew Stanton came to see a play I was doing three years ago at the National. God love him, he sat through a big Russian epic," he said.
"I met him afterwards and he'd seen [HBO drama] Rome and he wanted to use some of us, because he wanted these people on Mars - Jeddaks - to be almost Roman."
"I [then] realised that this is the Andrew Stanton who did Finding Nemo and WALL-E. Those were two of the most beautiful films I know - they touch adults and children alike."
Hinds confessed that Stanton has a challenge on his hands juggling the movie's huge visual effects demands.
"I think John Carter is going to be a difficult thing to pull off, but he's a very brilliant man," he commented.
"It's moving three different things. It's moving animation with computer digitalisation and real live-action. How you do that seamlessly I've no idea, and then how that reads through this big interplanetary story... it remains to be seen."
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Watch the John Carter trailer below: