"The flop of Asia," ran the private Daily Mirror's headline, while the state-run Daily News said one-day cricket had hit a "nadir".
The Island daily lamented the "sad night for Sri Lankan cricket".
Afghanistan demonstrated their rise in international cricket with their 91-run win over Sri Lanka in Abu Dhabi on Monday.
Sri Lanka needed to win the Group B match to stay in the tournament but were outwitted by Afghanistan who put up a fighting total of 249 all out at Sheikh Zayed Stadium.
Sri Lanka, who now have lost 30 of their 40 matches since January 2017, had lost to Bangladesh by 137 runs in Dubai on Saturday at the opening match of the tournament.
The Mirror said the performance did not augur well for the World Cup in England and Wales next year.
"Sri Lanka now require a great deal of soul-searching to be a competitive outfit in white-ball cricket before the 1996 World Champions become a laughing stock in the world -- if they aren't that already," the Mirror said.
Disappointed Sri Lankan fans took to social media to went their anger, with many memes ridiculing the national team.
"We could have stayed in the Asia Cup at least till India played its first match," said one social media user.
India's first game, against Hong Kong, was scheduled for later Tuesday.
Another social media user ridiculed batsman Kusal Mendis who was out for a duck, saying there would have been more cheer if a different "Mendis" was included -- referring to a popular alcoholic drink known as "Mendis Special".
Another fan speculated tongue-in-cheek that the poor performance was all part of a strategy to dupe other teams into thinking Sri Lanka were weak before next year's World Cup.