The 40-year-old seven-times world champion will start the sprint from 11th on the grid, unless he is penalised, and was almost lost for words after the session.
He was summoned to see the stewards for allegedly failing to slow under double yellow flags waved when team-mate Charles Leclerc spun late in the second sprint qualifying session.
The incident wrecked Hamilton's hopes of delivering a late flying lap to advance to the final sprint qualifier.
Without a podium finish in a record 20 races since joining Ferrari this year, Hamilton has been unable to sustain momentum in a season of frustration.
"It's not for the lack of trying," he said. "The team thought we were a lot faster than we are."
"I gave it everything and ultimately we're just not quick enough.
Leclerc qualified eighth.
"I am very disappointed," he said. "The car felt good, but it was just not fast enough."
"It felt slow."
