Despite dominating large periods of the match in St Petersburg, the Swiss carved out few clear chances and were beaten by a deflected shot from Emil Forsberg.
Speaking to reporters after the game, and quoted by Reuters, Petković said: "We are sorely disappointed, we wanted to do more."
Despite the unfortunate nature of the goal that they conceded, Petković admitted that his side simply hadn't given an adequate performance. "Sweden did precisely what they were good at and that was enough to beat us," he said, adding: "We should have done things better, but we were not good enough to win this match."
The 54-year-old also gave a more detailed explanation of Switzerland's shortcomings against the Swedes. "We wanted to play down the wings but we were too slow, our passes were not good," he lamented, adding: "We played out of defence too slowly and we also tried to play diagonal passes, but we were not good enough. We didn't find any fluidity."
Switzerland's loss to Sweden is only their second defeat in their last 16 competitive matches - the other one coming against Portugal in the qualifiers. According to FIFA rankings, the Swiss are the sixth best national side in the world - 18 places higher than the Swedes.
Petković said what many Swiss fans were also likely to be thinking: "Sweden are a strong team but we didn’t expect to be losing against them."
Switzerland's defeat means that they have now lost in the round of 16 in three of the last four World Cups. They last reached the quarter-finals when they hosted the tournament in 1954.