After 12 years in charge, Germany's head coach will be under intense pressure to resign in the coming days, despite having only signed a contract extension until 2022 last month.
“It's too soon for me to answer, it will take a few hours to see things clearly, the disappointment is very deep in me,” 58-year-old Löw said when asked if he will resign.
“We will have to have discussions tomorrow, we'll see how it goes.”
It is the first time Germany have failed to qualify from the group stages at a World Cup since 1938 as the holders became the latest defending champions to crash out early.
“This is a huge disappointment for us — there was deathly silence in the dressing room,” said Löw.
“Congratulations to our opponents, the Swedes and the Mexicans.
“We were rightly eliminated from the tournament.
“We had many goal possibilities, but we could not force the goal.”