The 25-year-old West Ham man was dismissed for elbowing Chilean counterpart Arturo Vidal seconds after clashing with Jean Beausejour 30 minutes into a tense encounter at the Nelson Mandela Bay Stadium. Behrami later protested his innocence, but will sit out the Group H finale against Honduras as the Swiss attempt to make the most of their opening victory over Spain to book their place in the last 16.
He said: "Of course my team-mates will go to the next round because we deserve that - and after this decision, we deserve better. It will come back for us. How I feel now is that it's destroyed my World Cup. A season like this, it's unbelievable. It surprised me because it's normal to have contact in football. My movement wasn't [intended] to create damage or do something to the player. I just wanted to protect the ball, like I have done every time. It's unbelievable for me."
Switzerland were already having to defend in numbers when Behrami's premature departure made their task all the more difficult. But Chile, who face the Spaniards on Friday knowing that their six-point tally may not be enough to take them through, had to wait until the 75th-minute for their winner, which came from the combination of two substitutes.
Esteban Paredes, who later missed two glorious chances to extend his side's lead, rounded keeper Diego Benaglio to cross for former Liverpool striker Mark Gonzalez, who headed home off the underside of the bar. It was tough on Benaglio, who had earlier pulled off three excellent saves to keep the Swiss in it, and his side might have snatched a point at the death when substitute Eren Derdiyok got a sight of goal, but dragged his shot wide.
Chile coach Marcelo Bielsa said: "We were in possession of the ball for most of the match and we had lots of goalscoring opportunities, but scored only one goal. We also had the advantage of playing with one more player than our opponents, but the match could have ended in a draw because only a few minutes before the end, they [Switzerland] had a very clear goalscoring opportunity. But I think the victory was deserved."
Swiss boss Ottmar Hitzfeld was unhappy with the sending-off, but admitted his side could have come away with a draw. He said: "We had a great chance in the 90th minute, and a 1-1 draw would have been the perfect result for us. It would have been deserved as well because we had to play 10 v 11 for 60 minutes, and particularly because the red card wasn't a red card, in my view."