Goals from Julian Quinones and Raul Jimenez gave Mexico victory at the Estadio Azteca, but Broos said the scoreline did not fully reflect his team's defensive performance against the co-hosts in front of more than 80,000 fans.
"You're playing a World Cup, you're playing against a really good team, but we played a good game," Broos told reporters.
"I saw a desperate Mexico. They didn't know what to do with the ball. The organisation was perfect defensively."
South Africa struggled to create chances and Broos acknowledged his side must improve in attack if they are to keep alive their hopes of reaching the knockout stage.
"Offensively I think we have to improve," he said. "If we can play the same game but be better offensively, then I'm sure we will have a better result."
Three red cards
The defeat left South Africa facing additional challenges after Sphephelo Sithole and Themba Zwane were sent off in a match in which Mexico captain Cesar Montes was also dismissed, the first World Cup openIng game to feature three red cards.
Broos accepted Sithole's dismissal for denying a goalscoring opportunity but questioned the decision that led to Zwane's red card.
"The first card I think you have to accept. The second, I think you can discuss because it is the Mexican player who blocks my player," he said. "But it's the appreciation of the referee and we have to accept it."
"We have two players who can't play in the next game but we still have other players and if we can show the same mentality and the same way we play today, I'm sure we will have good results in the next two games."
South Africa next face the Czech Republic in Atlanta, a match likely to determine whether they remain in contention for a place in the knockout rounds.
"We need the next couple of days to get over the disappointment and also the fatigue," Broos said. "But then we have to work on our offensive game because it wasn't enough today."