Ewan revealed the dental issue after finishing second on Sunday but was not using it as an excuse.
The Australian sprint ace was boxed in for the high-speed finish at Geelong and could not start his final run when he wanted.
He was catching the Italian star, who made the most of a perfect leadout, but ran out of road at the end of the 163.4km race.
After originally planning for a few days' training at Noosa, Ewan is now headed for surgery instead.
"It's not ideal, but I don't think it affected my legs too much," Ewan said of his wisdom teeth issue.
"It doesn't help, but I can't use it as an excuse."
Ewan also had a second-placed stage finish at the Tour Down Under last week and then controversially was relegated for headbutting after he won stage five.
"If I take the positives out of it, I know my form is quite good and my sprint's quite good," Ewan said.
"But at the end of the day, I'm here to win ... that's a little bit frustrating."
Ewan had strong backing from Viviani, who joined the list of cycling figures who say the relegation was too harsh a punishment.
Referring to Ewan's second-placed finish last year, Viviani also backed him as one of the main favourites for the March 23 Milan-San Remo classic, Ewan the runner-up in 2018.
Known as the sprinters' classic, it is the main early-season objective for Ewan and Viviani, the Italian also looking a hot chance in his home nation's Monument.
"He deserved the win in the Tour Down Under," Viviani said. "That's a sprint, there's nothing dangerous that happened.
"He's one of the biggest favourites for San Remo."
While Ewan leaves Australia feeling frustrated and nursing a sore mouth, Viviani is rapt.
He won stage one at the Tour Down Under and Sunday's win was 12 months in the making.
Viviani's runner-up finish a year ago was a rare blemish for the Deceuninck-Quick Step star, who racked up 18 wins for the powerhouse Belgian team nicknamed the Wolf Pack.
"Always when they ask me about my amazing 2018, I say there are two second places I don't like - this race and Gent-Wevelgem," he said.
Teammate Michael Morkov gave Viviani a textbook leadout at the finish after Dries Devenyns also did a power of work in the closing kilometres.
"This week, I've won two watches, but I probably need to buy another five or six ... my guys did an amazing job," said Viviani, referring also to his sprint classification win at last Thursday's Race Melbourne.
"After one month, we've been a long distance away from our families.
"That is the best end we can have."
South African Daryl Impey (Mitchelton-Scott) finished third.