Monaco GP: Mercedes can`t make any mistakes - Toto Wolff
Toto Wolff said: "It`s clear we are under attack from more than one angle.
"We cannot afford to drop the ball so we must remain united and strong, and hit back hard this weekend."
The crash meant Hamilton - who trails Rosberg by 43 points in the championship - fell to third in the table behind Ferrari`s Kimi Raikkonen, who finished second to Red Bull`s Max Verstappen in Spain.
Red Bull are expected to get a performance boost in Monaco this weekend, with one of their cars set to be fitted with an upgraded Renault engine that boosts performance by up to 0.5 seconds a lap.
Renault has not yet declared whether it will race the engine in Monaco, but the company is tipped to give one of the new engines to each of its teams - the factory outfit and Red Bull.
If they do, the most likely recipients will be Red Bull`s Daniel Ricciardo and Renault`s Kevin Magnussen.
Hamilton, who has had a difficult start to the season as a result of a series of problems, is also only nine points clear of Ferrari`s Sebastian Vettel and Ricciardo.
Wolff said: "Barcelona was tough to take. We came away upset at an opportunity missed - but this is racing.
"The drivers know how we operate. The team is responsible for giving them the best possible cars and they are responsible for getting the best out of them - and for bringing them home.
"When we let them down, we apologise - and the same goes the other way.
"It`s a pretty normal culture - we deal with setbacks together and we move on."
Each driver felt the other was at least partly responsible for the incident but Hamilton said he was keen to put it behind him.
He said: "Barcelona was the worst feeling but, like I always say, the true test is how you get back up when you`ve been knocked down.
"It was a tough moment for all of us after the race but it`s now chapter closed and looking ahead to Monaco."
The world champion is determined to clinch his first win there since 2008 having lost last year`s race in Monaco because of a team strategy error.
After dominating the weekend, he was called into the pits by mistake during a safety-car period and lost out to Rosberg and Vettel.
"It`s an incredible feeling making a car dance through those streets, one of the purest thrills you can have in a racing car," Hamilton said.
"I`ve not had the best run of results in Monaco in recent years - but last year showed I have the pace to do the job.
"I`m approaching this weekend with only one result in mind."
Rosberg, who has won the last three races in Monaco, added: "I was gutted after what happened in Spain - for myself, but mostly for the team.
"I know how hard everybody works to make these amazing cars, so for us to leave them both in the gravel is the worst possible scenario. But we`ve talked it through and now it`s time to leave it in the past.
"It`s one of my home races next in Monaco - the ultimate driver`s track. It`s where I grew up and where I still live today, so that always makes it a special weekend.
"It`s been amazing to win there for the past three years - but I know it will be tough to repeat that with Lewis, the Ferraris and the Red Bulls all so strong now. I`m feeling confident, so bring on the battle."