Hamilton and Mercedes struggled throughout the Monaco weekend, qualifying and finishing the race in seventh as Red Bull rival Max Verstappen took control of the championship race with his first victory in the Principality.
Former Mercedes driver Rosberg indicated the team missed a chance to promote Hamilton into the top five with its strategy error when choosing to try and undercut Pierre Gasly instead of running longer, with Sebastian Vettel and Sergio Perez eventually leaping both drivers.
"From the get-go, he never had confidence in the car," Rosberg told Sky Sports F1.
"In FP3 before qualifying, his rear was snapping all over the place, there were lots of mistakes out there and he never found the rhythm in qualifying, seventh place.
"But in the race, there was still a chance to get up there like Perez's position, P4.
"They rolled the dice, tried to go early but underestimated how difficult it was to warm up the hard tyres on exit and lost out to so many other guys."
Rosberg hails 'awesome' Verstappen
Verstappen took full advantage of Charles Leclerc failing to start to take a win from what was effectively pole position and his first championship lead since graduating to single-seaters from karts.
"[What a] fantastic weekend [Red Bull] have done," he added. "Max has delivered in the race awesomely and he had to.
"He had a couple of setbacks in the last couple of races where Lewis really had the upper hand, beat him on the track and now he is fighting back, leading the championship. For us, as spectators, awesome."
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