The Potters had an abundance of chances throughout the 90 minutes, but failed to respond to Nathan Ake's first-half header from a free-kick as they lost for the first time since September 18.
Bojan had his side's best chance, on just his fourth start of the campaign, winning a penalty in the opening stages of the second-half and stepping up to the spot himself only to hit the crossbar.
Marko Arnautovic and Xherdan Shaqiri were both guilty of missing chances, as were Bruno Martins-Indi and Jonathan Walters - as Stoke failed to make their second-half surge of momentum pay at the Bet365 Stadium.
But despite their wastefulness in front of goal, the Stoke boss says his side were deserving of more out of the game - and he also criticised the manner in which their opponents ran down the clock in the second-half.
Speaking afterwards at his post-match press conference, he explained: "We didn’t start great in the game in fairness. I thought Bournemouth came out with good intensity and good intent."
He acknowledged the confusion inside the box for Bournemouth's goal, calling it a "poor goal" to concede from their point of view.
The Welshman declared: "Sometimes when free-kicks are given in those areas, lads have a little bit of confusion in terms of whether they’re setting up for a corner or for a wide free-kick. I think Bournemouth were able to benefit from that. We just lost the man in the middle of the box, which is poor from our point of view."
Hughes felt that the game played into the hands of the visitors when they were 1-0 up, insisting their "good pace on the break" meant they "could play a counter-attacking game" and forced Stoke to "find a way."
But he added that his side showed "good heart" in the final minutes of the first-half, insisting they "started to drive the game" which "continued into the second-half."
We could've gone on to win had we scored the penalty, suggests Stoke manager
"We had any number of chances to get back on level terms in the second-half," he continued. "The clearest was obviously the penalty miss. That could very well have got us on the road to victory because at that stage we were really in the ascendancy and looking to capitalise on the chances we were making."
But Hughes accepted that "days like that" where "you can't take the chances" no matter "how long you play" are a part of the game.
He told journalists of the positives that Stoke can take away from what was a "difficult" game, insisting that his players "showed a lot of intent and a lot of good energy."
He praised the visitors for making it "difficult for us" and working hard "as a team" but also bemoaned Bournemouth for being "a little bit cynical in terms of their time-wasting."
The Stoke boss acknowledged that everyone has "been in those situations" as an "away side trying to protect the lead" and even said he has done it himself and is "not against it."
However, he insisted: "But I haven’t seen it to the extent that I saw it today to be perfectly honest. We played six minutes at the end of the game, it could’ve been 16 given all of the stoppages."
Hughes insists he's never seen time-wasting as "cynical" and "blatant" as Bournemouth's
On the impact that had on the game, he continued: "When you chase the game, clearly you want momentum. You don’t particularly want minutes at the end of the game. You want momentum and the game to flow to get some intensity in your play. That was difficult to maintain in the second-half because of the time-wasting."
Yet he was keen to emphasise that it represented no excuse for Stoke coming away with nothing, saying that "it is what it is" and that they "should've converted any number of good chances that we created."
"I felt our performance deserved at least a draw," he added. "Whether or not we deserved a win, that’s open to debate. But certainly, we didn’t deserve to lose the game."
Expanding on his point about Bournemouth's consistent determination to slow down the game, Hughes insisted that "everybody in the game has time-wasted to a lesser or greater extent" but said he hasn't "seen it quite as blatant, or for so long, as in that second-half."
He said that it "started from minute one of the second-half" as he explained: "It was clearly an intent that they were going to slow things down and go down and be slow on free-kicks, throw-ins and on every occasion. I haven’t quite seen it as blatant as that for many years to be perfectly honest."
But Hughes again repeated that Bournemouth's time-wasting was "not the reason we got beat" and that rather the fact they got themselves "in a situation that could've been avoided" was their downfall.
He said that Bournemouth's tactics simply "made it more difficult' to "have a performance and a result to match" as he said: "It’s not an excuse but it didn’t help what we were trying to do."
"We got away with one," admits Hughes after referee fails to award Bournemouth an early penalty
Hughes' opposite Eddie Howe was frustrated afterwards at the decision-making of referee Roger East, who he felt should have awarded Bournemouth a penalty early on when Ryan Shawcross brought down Callum Wilson in the box.
And the 53-year-old Potters boss admitted that they were forunate not to have had a spot-kick given against them.
"I've looked at that. It's a difficult one," he said. "Ryan’s made a genuine attempt to get the ball. Maybe the referee felt that the ball was a little bit out of the lad’s control, a bit away from him. Maybe that’s why, because the ball clearly ran through after the challenge. But yeah we got away with one there."
Hughes added that Bournemouth had "a few chances on the break" as his side were "pushing to try and get back on level terms" and left themselves "a little bit stretched" by players "committing and over-committing at the other end to try and get back on level terms."
Overall he felt that the result was a "little bit frustrating" because Stoke "showed good energy and tried to make things happen."
He felt that "on another day" they would have "got something out of the game" but implored his team to pick themselves up and "go again", adding: "It’s the end of a good run, we’d had six games unbeaten before this. It’s up to us now to go on another similar run if we can."