There has been nastiness between them leading to the bout, including an exchange of mild head butts at the weigh in, and he was irked that the media in Quebec was abuzz over a feature story dredging up Stevenson's past troubles with the law.
Add to it all that the 36-year-old from Montreal was physically worn down from having fought four times in a year — all knockout wins.
"I need vacation now," said Stevenson (23-1).
The fight card that started Saturday night and extended into Sunday at the Pepsi Colisee featured a pair of light heavyweight knockout artists who each gave the crowd of 8,540 what they came to see.
Sergey (Krusher) Kovalev (23-0-1), the WBO champion, took out Ismayl Sillakh (21-2) with a pair of thundering rights in the second round of the co-feature.
The five-foot-10 Stevenson took longer to hunt down six-foot-three Bellew (20-2-1), whose strategy was to keep his distance from the champion's crushing left hand and try to surprise him late in the scheduled 12 round bout.
It worked until the sixth, when Stevenson sent Bellew to the floor with a left uppercut. After the eight count, Stevenson drove the visitor to a corner and pounded him with at least three more power shots before referee Michael Griffin stopped the fight.
"He didn't want to mix it up," said Stevenson. "He just wanted to survive, moving left and right.
"I realized that, so I took my time, cut off the ring and soon I got my opportunity to catch him."
Stevenson was the heavy favourite, but there were no triumphant smiles as there was when he won the title in June with a KO of veteran Chad Dawson only 76 seconds into the first round or his seven round win over former champ Tavoris Cloud in September. He also had a six round win over journeyman Darnell Boone in March.
"The guy tried to get me off my game," said Stevenson. "He gave me a head butt (at the weigh in).
"In the ring, I wanted to knock him out. I said fourth round. I did it in six, so there's not much difference. I wanted to knock him out and show him that I'm the champion. He's not the champion and never will be."
The 30-year-old Bellew had his moments. He caught Stevenson on the nose with a sharp jab in the second, and thought he had scored a knockdown in the third, but it was ruled a slip.
"I could see the left hand coming all night, but the one that caught me I didn't see," said Bellew. "In boxing, the one you don't see is the one that hurts you.
"I thought I'd knocked him down in the third, but the referee didn't score it. That's why I tried to pressure him. He's very clever when you pressure him. He looks for an opening. One thing I'd say about him is he's very hard to hit."
His promoter Eddie Hearn said Bellew would learn from a loss to what he called "the best fighter in the division" and will take another run at a world title after a few more fights.
"Adonis was more elusive than he thought," said Hearn. "Tougher to hit than he thought.
"He took a lot of good shots. Tony's got a great chin, and then took one too many. Then, after a while, he tried to trade with him and unfortunately when you trade with a puncher like Adonis you're in trouble."
Stevenson said it had been a difficult week, partly because of a feature that appeared a week earlier in Montreal La Presse detailing his life in a street gang in the 1990s. Stevenson spent 20 months in prison for pimping, assault and other charges.
Since his release, he turned to boxing and has stayed out of trouble. There have been many boxers with criminal pasts over the years, and Stevenson was miffed that so much attention was paid to his case.
He said he will talk to his family about going to live elsewhere, although he already spends much of his time training in Detroit at the Kronk Gym under Javan (Sugar) Hill, nephew of hall of fame trainer Emanuel Steward.
"This week, people brought up my past," a surly Stevenson said. "That was 17 years ago. "And they tried to do everything to try to lose my concentration so I wouldn't win. I'm going to take time to reflect, with my family, on whether we will leave Quebec."
"When young people see that — where I've come from and then people still put me down — it doesn't make sense. You can call that racism."
He will still have Yvon Michel as his promoter and likely will continue to fight in Montreal, where his fan base is centred. But he said it is up to Michel and the U.S specialty channel HBO where, and against whom, he fights next.
Given the choice, he'd like to face Bernard Hopkins, the 48-year-old who is still confounding opponents with remarkable defence and ring savvy.
He said he can wait for Kovalev, which many want to see — a showdown between a righty and a left-handed knockout specialist.
Kovalev and Sillakh felt each other out for one round, then the Russian caught him with a right. Kovalev was jumping up and down in a neutral corner during the eight-count, then ran across the ring and put him down and out with another big right.
Asked if he was hoping the ref would stop the fight or let it go on, Kovalev grinned and said "I wanted it to continue and punch him again. He said a lot (that was) not polite to my side a long time ago. He said I'm nobody. I say 'you see who is body, who is nobody.'"
It was Kovalev's first defence of the title he got with a fourth round win over Nathan Cleverly in August.
The 30-year-old also fought four times in 2013, and his promoter Kathy Duva said he should be considered for the fighter of the year award for winning four times by KO in under 12 rounds.
Stevenson's promoters say the same for their fighter, who is the lone Canadian with a world title.
The best fight of the night saw Ionut (JoJo) Dan (32-2), a Romanian based in Laval, Que., win a split decision over Quebec City's Kevin Bizier (21-1). One judge had it 117-110 for Bizier, while the others had it 116-111 and 114-113 for Dan, who had a questionable point deducted in the 10th for holding.
At stake was the No. 2 ranking in the IBF, where Devon Alexander is champion.
A rematch is highly likely.