The British rocker - who is engaged to Kate Moss - claims his bandmate Alison Mosshart's involvement with Jack's group The Dead Weather affected the recording schedule of the duo's fourth studio album 'Blood Pressures'.
But he accepts her experience with former White Stripes guitarist improved her as a musician.
He explained: "Obviously The Dead Weather stuff affects what I'm doing, and I would have been happier making a Kills album earlier than this, but all those problems are eclipsed by what it did for Alison.
"I really noticed the change in Alison's voice when she came back off tour with The Dead Weather. It had become so strong. There was more confidence there."
Alison insists it was "accidental" that she ended up dedicating so much time to The Dead Weather.
She explained to NME magazine: "It was just loads of accidents and trying to come up with a strategy about how to get things out there without stepping on people's toes. There was never a game plan.
"I would've liked not to have had three years off from The Kills but in the end there isn't enough time in the day, and me and Jamie are really pleased with 'Blood Pressures'. It's just whatever it takes to get there, y'know?"