And they face a big battle to improve on their recent continental campaigns after being drawn against triple European Champions Leinster, in-form English giants Northampton Saints and TOP 14 title winners Castres Olympique in Pool 1.
"We're the perennial underachievers in the Heineken Cup and always get the pool of death because we have underachieved. It's always going to be a hard pool because the best sides are in this competition," said Jones, whose team were beaten for the first time this season on Friday.
"I regret saying we've under achieved, not because of the sentiment but because everybody's used it in a question to me. It's not something we want but the tagline has already been put on us and our pool because we've under achieved in the past.
"That's because we've been honest with the media and with ourselves and said 'look, we have under achieved and drawing a line in the sand and moving on is par for the course in starting success'.
"The Heineken Cup is like a second start to the season with players coming back and a new competition. As long as we translate the form we've had in the Rabo into the Heineken, we'll be pretty close."
The Ospreys kick off their latest challenge at home to Leinster on Saturday, with victory likely to be crucial to their hopes of making it through the pool stages.
And while it is the Irish outfit who have the more enviable European record, the Ospreys have twice shocked Brian O'Driscoll and co in domestic finals in Dublin and drew 29-29 at the RDS in Round 2 of this year's PRO12.
And Jones insists it will be those past experiences his team will look to benefit from, rather than attempting to find any extra motivation in the close relationships he and Ian Evans, Richard Hibbard, Adam Jones and Justin Tipuric established with Leinster's Lions contingent during the summer series in Australia.
"I don't think that adds anything extra. It'll be the rugby perspective rather than the social side that will be crucial for us," added Jones.
"Our record against them is pretty good and we know a lot about them, just as they do us. We've done pretty well against them in a couple of Rabo games when we weren't expected to.
"Both us and them will probably field stronger sides for the first hit out in the Heineken Cup. They've got a bit of depth at 10: is it going to be (Jimmy) Gopperth or is it going to be (Ian) Madigan, so there's a little bit of the unknown for us in that regard."
There's very little sense of unknown for the Ospreys within their own squad, however, with Jones believing the home grown nature of so many of the current crop of Ospreys, coupled with summer signings who may have flown under the radar or arrived in Swansea with something to prove, leaves the Liberty Stadium side in a good place to kick on in Europe.
"We're fortunate that we've got a lot of boys who were coached by Steve (head coach Steve Tandy) when Steve was at Bridgend and they've come through now, have had a taste of regional rugby and are adding to our strength in depth.
"You add that to the signings we made like Jeff Hassler, Ty Ardron, Tito Tebaldi etc, and it's nice to have players who add to the culture and the social side and do the business on the park. If you get that, you're pretty fortunate.
"You've then got the likes of Rhys Webb and Hanno Dirksen hoping to feature before or around Christmas and that's a pretty exciting prospect. We can rebuild our reputation, the way we've rebuilt our squad."