The 2009 champions won once, against Bangladesh, and suffered defeats by India, New Zealand and Australia.
The team were jeered on their return to Lahore airport, with huge crowds chanting "Shame! Shame!"
Former fast bowler Waqar said: "If my leaving makes things better, then I would do it without delay."
Waqar is in charge as head coach for a second time and his current contract ends in May.
He added: "When there is no cricket at home [because of security concerns in Pakistan] then the foundation will for sure become weak. I place my hands together and beg forgiveness from the nation."
Captain Shahid Afridi, 36, is expected to announce soon whether he will be retiring from internationals or not.
Pakistan head coach Waqar Younis has "begged forgiveness from the nation" after the side's group-stage exit from the World Twenty20.