The Cherries won their first Premier League away game since April courtesy of Nathan Ake's first-half header, but were denied what looked a stonewall penalty inside the first 15 minutes.
Callum Wilson was brought down by Stoke's last man Ryan Shawcross as he raced into the box, but the referee gave nothing to leave the visitors frustrated at the Bet365 Stadium.
Ake's header gave Howe's side the advantage mid-way through the first-half, but they were fortunate first to Steve Cook for his clearing header to deny Shawcross before the break and then to the crossbar just after half-time to stay level.
Bojan won a penalty after a tangle with Cook after 48 minutes, only to cannon his attempt from 12-yards back off the crossbar.
Bournemouth ultimately hung on for a priceless three points, their first ever victory in the Potteries, but Howe feels not only should his side have had a penalty - but that Stoke's spot-kick shouldn't have been awarded either.
Speaking in his post-match press conference, he insisted: "At half-time I tend to focus on the team and what I can change in the second-half. I don’t think there’s any point chasing officials or making your point that way.
"But I will be speaking to them on Monday morning to get clarity on the decisions because I felt the two big decisions in the game, he [the referee] got wrong."
The Englishman explained that Shawcross' tackle on Wilson was a "clear penalty" and said he felt that Stoke's penalty wasn't one, adding: "It’s hard enough coming here when you get the decisions right and even more difficult when the major ones go against you."
Away win was "long overdue" admits Howe
But nevertheless, Bournemouth claimed their first away win of the current campaign and their first in eight months - which was more than welcome to the manager.
"There’s a sense of relief and satisfaction afterwards for a brief time," he said, calling himself "so pleased" for the players to come away with a "thoroughly deserved" win from a "really tough game."
Howe continued: "It’s nice to put that [statistic about not winning away from home] away because you don’t have to keep talking about it."
The 38-year-old declared that his team's away form last term "was really good" and expressed his surprise that it has taken them so long to win away from home this season.
He noted that they were "very close" to winning away at Crystal Palace, calling it "hugely frustrating" to be "seconds away from winning that game" and saying that to come and win at Stoke was "long overdue."
Howe further acknowledged that the win was made all the more important with fixtures against Arsenal, at home, and Liverpool, away from home, now to come.
He insisted they were "well aware" of their fixture list but said: "It’s a funny league. We had Middlesbrough and Sunderland and everyone was saying we’d got some easier games, but there’s no such thing as an easy game in this league."
Instead, Howe said that he is "well aware" of how "tough" every game in the Premier League is, insisting: "Sometimes you can surprise yourself against the top teams as well. There’s very little between the teams. So we'll enjoy these two games on the back of this win."
Ake didn't "put a foot wrong", says Cherries boss
Howe was also ecstatic with the contributions of goalscorer Ake, who made just his first start of the season as he replaced the suspended Adam Smith.
The manager felt the 21-year-old, on loan from Chelsea, was "exceptional" given that he "hasn't had a lot of football" recently.
He said that it wasn't "easy" to "step in in this kind of game" and added: "I don’t think he put a foot wrong. He scored a really good goal as well."
He extended his praise to Steve Cook, insisting he and Ake were both "excellent", and said it wasn't easy for the latter and goalkeeper Adam Federici to come in and "do that."
"All those lads that came in today did their reputations and their chances of featuring again no harm at all," Howe added.