Paraguay triumphed 4-3 on penalties following the 1-1 draw on Monday night as Germany crashed out of the World Cup in dramatic fashion.
Germany have not won a World Cup knockout tie since winning the competition for a fourth time in 2014 and failing in the Round of 32 will be particularly heartbreaking for fans who made the trip across the pond.
The loss to Ecuador in the final group match prompted concerns that Germany was ill-prepared for a deep run in the tournament, concerns that were proved to be correct.
Having won all four of their World Cup shoot-outs, Germany failed to impress from the spot in what was a poor performance that Kimmich believes is purely down to his side.
“We deserved to be eliminated. It feels terrible.
“We struggled badly in all three matches against teams that aren't world-class.
“We, the players on the pitch, messed up and we assume the responsibility.
“It wasn't the coach, it wasn't the media, it wasn't the referee, it wasn't the opponent. It was just us.”
The result places Paraguay among the World Cup's last 16 as they prepare to find out who they will face out of France of Sweden in the next round.
For Germany as well as fellow European side the Netherlands, they head home early as they watch the rest of the World Cup from home.