World champion Vettel was poised for his fourth win of the season in his Red Bull before he was forced to drop out with only 10 laps of the 52-lap race left to complete at Silverstone.
"When Sebastian stopped, to be honest, I won't lie, I wasn't disappointed by that one," Rosberg, who celebrated his 28th birthday on Thursday, told reporters.
Rosberg also profited from the misfortune of British favourite Lewis Hamilton, his Mercedes team mate, who started on pole position and led in the early stages before a tyre blowout relegated him to last place. Hamilton finished fourth.
"With Lewis, definitely I feel sorry for all the British fans," added Rosberg, the son of former world champion Keke Rosberg.
Rosberg's win still had a local flavour because the Mercedes team is based close to Silverstone in central England.
It looked like he might be stripped of his victory on a technicality but race stewards opted only to reprimand him for failing to slow down for yellow warning flags in a race marred by a series of tyre blowouts.
Rosberg won in May in Monaco, where he lives, and is looking to repeat that on German soil next weekend.
"I'm very proud to be German, driving a Silver Arrow, going to the Nuerburgring," he said.
Vettel still leads the drivers' championship on 132 points, ahead of Spaniard Fernando Alonso on 111.
Alonso was pleased to finish third on Sunday and close the gap on Vettel but was worried about the sluggish showing of his Ferrari.
"The pace we saw this weekend is not good enough," Alonso said. "Today we recovered some points but we know there is a lot of work to do."
Australian Mark Webber, who is leaving Formula One at the end of the season, said farewell to Silverstone with second place behind Rosberg.
"It was a nice finish to the race," the Red Bull driver said. "It would have been about 100 cherries on top if I'd managed to get past him but I didn't."