Red Bull's championship leader came second behind his fellow German in a race that ran like a procession through the Monaco streets in the early stages as drivers sought to manage the tyres to make a one stop strategy work.
"I was a bit surprised by the slow pace in the opening laps," Vettel, who had started behind the two Mercedes of Rosberg and 2008 champion Lewis Hamilton on the front row, told reporters.
"Usually you expect two silver arrows in front of you and there were two buses today going for a cruise - at least in the first couple of laps. But obviously the strategy was clear and they did a very good job.
"They were going quite slow and trying to obviously make the one stop happen. And fair play, they were in the lead, around here it's very tricky to pass."
Australian team mate Mark Webber agreed that the pace "wasn't electric" and the race "not super-exciting" until crashes wrecked the pre-race planning by forcing the introduction of the safety car as well as halting the race for 25 minutes.
Most drivers re-started the race on supersoft tyres and made them last for the remaining 32 laps.
"It was just basically saving tyres and making the one-stop work. It was completely predictable that if the race was going to stack up then the two-stop was not really an option to come back into traffic," said Webber.
"So we had to go very long, all the drivers were nursing the cars very aggressively...it was measured, controlled aggression, if you like, trying to nurse the tyres as best you can."
The quick-wearing Pirelli tyres have been a constant bone of contention this season, with the previous race in Spain won by Ferrari's Fernando Alonso after a four stop strategy that proved the norm.
Monaco, a tight and twisty track that is kinder on the tyres, is extremely difficult to pass on and puts a premium on pitting as little as possible so as not to lose position and get caught in traffic.
Rosberg, the first son of a Monaco winner to also win the glamour race, had been concerned about the tyres from the moment he qualified on pole position.
He had also started the last two races on pole without winning either as Mercedes failed to translate their one lap speed into long run performance, with the car particularly heavy on the tyres.
"In the last couple of races it was pole position and dropping back so much. There was always that a little bit in the back of my mind today in the race," he said.
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