Paraguay coach Anibal Ruiz described his team's World Cup exit as "deeply painful" after their 1-0 defeat to Sweden on Thursday.
The South Americans had looked destined for at least a draw before Freddie Ljungberg headed a winner in the penultimate minute of the match.
Ruiz said: "Sweden had more chances to score, they had more possession.
"It hurts but we have to congratulate the other team. Let me say that it is really deeply painful."
Paraguayan striker Roque Santa Cruz said only one aspect of their game had halted them from winning.
"We played a good match, we tried hard, but what was lacking was that last pass, that last push that you need to score," said Cruz.