The 'Do I Wanna Know?' band headlined the festival in Southern England for the second time on Friday (28.06.13) and the frontman felt it was one of the best shows they've ever done.
He told NME magazine: ''It's one of the best gigs we've ever done, ever.
''This is the best it gets! You only ever do, like, five gigs like this. And that one was the one. You do big shows, big festivals all the time, but it's a different beast, Glastonbury.
''We'll carry on playing to a lot of people all over the summer, but it won't have that feeling we had just then. That feeling I can't describe. It felt like I was in outer space.''
Alex's bandmate, bass player Nick O'Malley, shared his sentiment, adding: ''It felt like I was floating when I was up there [on stage], like I had roller blades on or something.
''Honestly, I thought I'd be sh*****g it, but I just felt really calm, strangely calm.''
While Arctic Monkeys - which also includes Jamie Cook and Matt Helders - were pleased with their performance, Alex came under fire for appearing to have lost his native Yorkshire accent, for a more American-influenced sound - although he appeared nonplussed.
He said: ''Maybe it's just my quiff confusing people? [Radio presenter] Jo Whiley just said I was channeling my inner Elvis, but I don't know man. It's not intentional.''
The novel's author saw a cut of the film and loved each of the changes the movie's director had made.