''We need to make sure that we're bulletproof,'' Rosberg said after Daniel Ricciardo passed the hobbled Silver Arrow with two laps to go to win the Canadian Grand Prix on Sunday.
''Having lost the win, that's very, very disappointing, definitely, and also disappointing for us as a team. We have such speed and such a great car, to not win the race and even just finish with one car and come second is hugely disappointing for us, definitely.
''Our ambition is to finish one-two so we need to make sure that we get back there again next race in Austria.''
Mercedes had won every race in the series heading into Montreal, with Rosberg posting two victories and four second-place finishes. Hamilton won the other four races, finishing second in Monaco last month; he had engine trouble and did not finish the season opener in Melbourne.
That's pretty much what it takes to knock the Mercedes off the top spots of the podium, and it happened again this week on the Circuit Gilles Villeneuve.
Both Rosberg and Hamilton had the same problem, at about the same time - the midpoint of the 70-lap race.
When Rosberg radioed in for a solution, he was told, ''We don't think we can resolve it.''
Rosberg said the problem put more pressure on the rear brakes, causing them to overheat.
''I think it surprised us, yes, because the pace Mercedes has had all year,'' Ricciardo said. ''Obviously, I'm still going to take the victory, don't get me wrong. But they had their issues today, which allowed us to really make an attack.
''But it's nice that we capitalized on that. I think it would have been disappointing if they had their issues and they were able to still get the best of us.''
The second-place finish - his seventh podium in seven races - gives Rosberg 140 points of a possible 175 on the season; Hamilton is second with 118.
Ricciardo moved into third with 79 after his first career Formula One victory, passing Ferrari's Fernando Alonso (69 points), and Ricciardo's Red Bull teammate Sebastian Vettel, the four-time defending world champion, finished third and is fifth in the standings with 60 points.
''We are fully aware that Red Bull is still an amazingly strong team and pushing like crazy to catch us,'' Rosberg said.
''We are well aware of that and we are always concerned and always making sure that our drive remains exactly the same as it was last year when we were half-a-second behind them. We're really pushing to even extend the gap.''
Vettel said he is feeling better about his car, but he won't let the two spots on the podium mask the fact that the Mercedes has been faster all year. And he's not counting on more mechanical problems for Rosberg and Hamilton in the future.
''Today, I think we got lucky,'' said Vettel, the 2013 Montreal winner. ''Obviously, it feels great and it's a great reward for the whole team after such a painful winter and a very difficult start to the season. To get both cars on the podium and to beat at least one of the Mercedes, I think that's a very, very positive day for us.''
Ricciardo has two third-place finishes, two fourth-place finishes and a win in his last five races. He crossed the finish line second in the season opener in his homeland, but was later disqualified for an illegal fuel flow.
Still, the 24-year-old Australian said it is too soon to the Grand Prix of Austria on June 22.
''I think I'll just enjoy this for now and not look too far ahead,'' he said. ''I think this is definitely a moment I should embrace. I'm actually supposed to fly back tonight, but I don't know if I want to spend (the night of) my first victory on a plane.''