The group scored five top five hits the UK between 2005 and 2007 - including number one 'I Bet You Look Good On The Dancefloor' - but none of the three singles from their last album, 'Suck it and See' made it into the top 40 and songwriter Alex thinks he's unable to pen a successful record because the musical "landscape" has changed.
When asked about chart success, he said: "I have f***ing forgotten how to do that. I don't know what that is any more, it's a different landscape these days."
The 25-year-old star also insists singing never came "naturally" to him and he is still "working on it".
He added to The Sun newspaper: "I was never a singer. I have had to practice at that and writing melodies is something that didn't come naturally. I was more comfortable writing lyrics.
"I am still working on it but I think we are getting there with the singing thing."
Alex wrote his first solo record, a six-track soundtrack for British movie 'Submarine', which was released in March this year and he also has his The Last Shadow Puppets side project with his friend Miles Kane.