The Welsh region made it a perfect five from five last Friday night with a hard-fought 15-14 win at Italian side Zebre.
But with European rugby set to return soon Jones, who has not made it out of the group of Europe's top-tier competition since 2010, is confident the best is yet to come.
"It will be a big step-up, it's almost like a season within a season," he said. "It starts again for us now and that is the mentality we need.
"It would be very nice if we could translate our form from the GUINNESS PRO12 into this competition.
"The way we have gone about the PRO12 we have been pretty honest with each other and with ourselves.
"In terms of the performances we have made I think a couple of the scorelines have been quite flattering to us.
"We have been our own worst enemies at times and that has forced us to leave some points out there on the park.
"We will be on our guard when we go into European competition to not get too carried away, to keep our feet on the ground."
In this, the second year of Steve Tandy's tenure as head coach the Welsh region look to have made significant improvements.
Last year Ospreys missed out on the top four and the Welsh international lock admits it has taken time for he and his teammates to come good.
"Steve has been able to recruit a back-room staff he wanted, they hold a big influence and that starts rubbing off on players," added Jones.
"We have got a good environment at the moment and are training with a purpose.
"It doesn't go right all the time, there are kinks in the game."
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