The 33-year-old actor - who played the web-slinging superhero in two movies between 2012 and 2014 - was thrilled to land the role of Peter Parker and his alter ego but had to do a lot to "fight for his freedom" while working within the Marvel Comics universe.
He said: "I was really excited to be Spider-Man. I had a real hope that it would be something that young people could connect with, that wasn't just about commodifying everything.
"But I had to fight a lot for my freedom within that. And I'd often get in trouble as I'd say things I wasn't supposed to."
Though Andrew - who previously dated Emma Stone - loves his job as an actor, he isn't a fan of the surrounding public interest in celebrity culture.
He told Mr. Porter: 'You just need to go home and be with friends, be with family. But I'm still learning, to be honest. I love being an actor, but I'm not crazy about celebrity culture."
Andrew can next be seen in true-life tale 'Hacksaw Ridge', in which he plays Desmond T. Doss, who became the first conscientious objector in US history to receive the Medal of Honor.
And the actor admits making the movie, which is directed by Mel Gibson, gave him a lot of perspective on his own life and caused him to question the values of society.
He told Mr. Porter: "When you look at Desmond Doss and then you look at our generation, you do ask questions. What do we value?
"Is it service, humility, our capacity to love, our capacity to be true? Or are we going to honour and value physical attractiveness or braggadocio or arrogance?"