The Welsh side were beaten 33-27 but claimed two losing bonus points, as they did in November's defeat by Clermont Auvergne.
Ospreys remain top of Pool 2, but Wales second row Jones was frustrated with the result.
"It [two points] is still probably not enough if we're honest," said Jones.
"We were the architects of our own downfall in the first half and in the grand scheme of the game really.
"After we went behind we had to chase and that cost us at the end of the first half but then probably rewarded us in the early stages of the second half."
Jones, 30, scored Ospreys' third try as they fought back from 30-15 down to cut Bordeaux's lead to 30-27.
The visitors played an attacking and loose style of rugby throughout, which proved productive and costly in equal measure.
Although they scored four tries to secure a bonus point, wayward Ospreys passes also led to two of Bordeaux's four scores.
"You're damned if you do, damned if you don't," said Jones.
"It's finding a happy medium. At times we were over-exuberant in the first half and a bit naive in the second.
"We're not going to blame the powers that be but we feel a little bit hard done by, particularly with the number of times we visited their 22.
"But then again we were the architects of our own downfall when we did do that."
Ospreys are two points clear at the top of Pool 2, with second-placed Exeter away at Clermont Auvergne on Sunday.
On his side's chances of reaching the quarter-finals, Jones added: "It's wide open really, so it should be good."

They were among a group of suspects acquitted in Kenya last week.
Taiwan's foreign ministry says they were forcibly put on a China-bound plane and has demanded their release.
China has not responded in detail to the allegations, but has criticised Taiwan for not considering itself as part of "one China".
The incident comes as cross-strait relations are feared to be entering a rocky period, say the BBC's Cindy Sui in Taipei.
Taiwan said the eight were among 23 Taiwanese people who were accused in Kenya of being members of a telephone fraud ring, which also included Chinese nationals.
They were arrested in Kenya at the end of last year and charged with illegal entry and telecommunications fraud.
All of the Taiwanese, and some Chinese, were later acquitted.
The Taiwanese were detained when they went to a police station last week to retrieve their passports.
On Friday, eight of them were put on a plane by Chinese officials and sent to the mainland, despite a court order that would have kept them in Kenya, say Taiwanese officials.
Taiwan has demanded their release, as well as for the release of the remaining 15 Taiwanese still in Kenyan custody.
On Monday, Taiwan's foreign affairs ministry accused Chinese officials of "obstructions", including delaying the court order and preventing Taiwan's representative from reaching the acquitted.
It said China's actions amounted to an "uncivilised act of extrajudicial abduction" which represents a "gross violation of basic human rights."
In response to a reporter's question on the matter, China's foreign ministry spokesman Lu Kang said: "I might need further understanding of the exact details of the case, but in principle, countries which follow the 'one China' principle are worthy of approval."
Beijing has refused to have dialogue with Taiwan's incoming President Tsai Ing-wen unless she recognises the two sides as part of one country.
Chinese President Xi Jinping and Taiwan's current President Ma Ying-jeou held historic but largely symbolic talks in Singapore last November, the first between China and Taiwan's leaders in more than 60 years.
Ospreys were the "architects of their own downfall" in their European Champions Cup defeat at Bordeaux-Begles, says captain Alun Wyn Jones.
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Taiwan has accused China of "extrajudicial abduction" after eight Taiwanese acquitted of fraud in Kenya were deported to mainland China.