The team, captained by Shahid Afridi, beat Bangladesh, but lost to New Zealand, Australia and arch-rivals India.
"I place my hands together and beg forgiveness from the nation. If my leaving makes things better, then I would do it without delay," Younis told a news conference.
The 44-year-old former pace bowler is in his second spell as Pakistan coach, having first held the job between March 2010 and August 2011.
(Reporting by Simon Jennings in Bengaluru, editing by Ed Osmond)
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