The band reached number two with their latest album The 2nd Law on the Billboard 200 chart, but confessed that they want "something more".
"Coldplay are the only English group to have had real success there in the last 15 years," Matt Bellamy told the Daily Star.
Bassist Chris Wolstenholme added: "You don't think about it when you start, you're just content to be recognised on home soil. But then you want something more."
Bellamy also joked that they have yet to master writing and recording a quieter, stripped-back song.
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"I'm disappointed that we don't have many acoustic tracks, more quiet moments," he said. "When I left the studio after having laid the foundations for the single 'Madness' it was sparse.
"When I returned two days later, Chris and Dom Howard had put absolutely everything on it."
Muse's latest album The 2nd Law topped the UK chart on Sunday (October 7).
Watch the music video for Muse's 'Madness' below: