The Tigers meanwhile found themselves overpowered in the second half as they fell to a 23-9 away defeat to European powerhouses Toulouse.
But despite their opening defeat Jones knows better than to write off the two-time European champions, especially at Welford Road.
"We know the size of the Leicester challenge," Jones, who played in Ospreys' thrilling 32-32 draw at Welford Road back in 2009, told Wales Online.
"We've been up there and drawn there, so we know we've come close in the past.
"We realise the quality they have, the kicking game and the forward pack.
"They're the complete package and they'll be baying for blood because they probably feel they've under-achieved in this competition for a while.
"So we're very aware of the threat they pose, especially at home."
While the Tigers have not made much of an impression in Europe since losing in the final to Leinster back in 2009 it has been a similar story for the Ospreys who have failed to make it out of their pool for the last two years in succession.
And Jones insists his side are itching to set the record straight this time around.
"The last two years we've fallen short of the standard required in this competition, and people are probably writing us off," Jones added.
"But we'll just keep plugging away and if we can get a good team performance then anything can happen.
"We are not the finished article, we are going to keep working.
"We are conscious that there are areas where we need to improve so there is work to be done - but we are moving forward.
"What we have to do now is go to Welford Road and play even better against Leicester.
"Beating Treviso was pleasing because they have caused us problems in the past."
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