"I am resigning from my post with a heavy heart," said the 44-year-old former fast bowler, who has ended his second spell in charge.
The 2009 champions won once, against Bangladesh, and suffered defeats by India, New Zealand and Australia.
Waqar's resignation comes a day after Shahid Afridi, 36, stepped down as Pakistan's Twenty20 captain.
The team were jeered by a huge crowd at Lahore airport on their return from India.
Then, in his post-tournament report to the Pakistan Cricket Board, Waqar blamed Afridi's "poor captaincy" for the team's performance
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In a critical six-page document, Waqar said he did not want to "shift the blame to any personal individual but to identify where things did not go right".
However, despite Afridi's resignation, Waqar has stepped down three months before his contract was due to expire.
It ends his second term in a post he has held since 2014, following a first spell in charge between 2010 and 2011.
Afridi, the world's leading wicket-taker in T20 internationals with 97, planned to retire from international duty at the end of the tournament but has now said he wishes to play on.
A hard-hitting right-handed batsman and leg-spinner, he retired from Test cricket in 2010 and from one-day internationals in 2015.
Waqar Younis has resigned as Pakistan head coach following his side's group-stage exit at the World Twenty20.