Pakistan failed to clear the group stage and the campaign included a six-wicket defeat to arch-rivals India.
Addressing a press conference at the Pakistan Cricket Board headquarters here, Younis said: "I place my hands together and beg forgiveness from the nation."
The legendary fast bowler, who was hired as coach for a second time in 2014 and whose contract is due to expire in May, added that he was prepared to stand down if it was in the team's best interest.
The 2009 champions have been widely blasted by fans following their lacklustre performance with just one victory against lowly ranked Bangladesh.
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The cricketers returned to a hostile reception in Lahore and Karachi after their campaign, which also included big losses against New Zealand and Australia, came to an abrupt end.
Team members were jeered on their return this weekend by huge crowds who chanted "Shame! Shame!"
Waqar also called for a revamp of the country's domestic structure, and added that the malaise stemmed from Pakistan's lack of home games since 2009 terror attacks on the Sri Lankan team.