Nigel Pearson believes a penalty decision wrongfully turned down was the key moment in the contest but praised his team's doggedness against a side on the brink of the Premier League.
Chris Martin was clumsily bundled down to the ground by Lloyd Kelly in the second half with Bournemouth 2-1 ahead. 18 minutes later, Siriki Dembele ensured the points would remain on the south coast when he fired in the third.
Rob Atkinson threatened to upset the odds after just four minutes when he met Matty James' corner, thumping his header past the outreaching Mark Travers to send the travelling fans into raptures.
City's resolute defence was eventually breached five minutes before the half-time whistle when Jordan Zemura found space on the left and his cross was turned in by Dominic Solanke from close range.
There was a question mark over whether the striker was in an offside position but the linesman kept his flag down despite the protests of the City backline.
Seven minutes into the second half and the visitors found themselves behind when Lewis Cook's strike from distance beat Dan Bentley at his near post.
Dembele made it three when he cut inside Alex Scott and Timm Klose on the left before Andi Weimann scored his 19th goal of the season when he gave the visitors a glimmer of hope at the end.
City's away record now stands at one win in their last 14, but Pearson believes the scoreline could have been different had the referee pointed to the spot just after the hour mark.
After the game, he said: "Well, I’ve seen it from different angles and if we hear the term ‘a natural coming together’ again, my interpretation of the law is that defenders can’t touch a forward from behind and make physical contact.
"It’s not a coming together because Chris [Martin] has touched the ball away from him. We’ve had one penalty all season and we’ve had so many decisions go against us, it’d be interesting to know why. I couldn’t give you an answer to that.
"I can’t say anything about it I’m afraid, the officials aren’t publicly accountable."
Pearson admitted there were a lot more positives than negatives throughout the display, albeit bemoaning a lack of quality in possession in the first half, but ultimately they came unstuck against a side who deserve to be playing top-flight football next season.
He added: "(We were) Committed. I thought we defended really well in the first half in terms of keeping a shape, a good shape, you can see the quality they’ve got so we needed to try and combat that.
"Getting an early goal gave us a situation to defend but unfortunately we gave the ball away too many times in the first half.
"I think it was 14 times we turned the ball over when we had comfortable possession which means that we were defending for much longer. That was our problem but I also recognise that that is born out of playing a good team.
"They’ve got a lot of players who have played in the Premier League before, they’ve got a big squad and lots of quality but we gave them a really good game today. There’s still things that we’re disappointed with of course.
"I thought we showed some good qualities today but we made too many unforced errors in possession.
"We’ve conceded three more goals and that’s why we are in the position that we’re in, because we can’t keep enough clean sheets. We’ve proven that we can be a threat in terms of creating chances. That’s where we are. We were in the game today.
"One thing you need to understand and well today is that physically they are up there at the top of the league, they are top of the league with physical stats. Not only do we play against a side today that are technically very, very capable, they’re very, very fit too. That’s a reflection of again the Premier League history.
"If players are committed to the performance then you’ve always got a chance of getting something. I would imagine their dugout was relatively pleased when the final whistle went because anything can happen.
"We’re disappointed, but I’m also realistic about the situation too."
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