It is a similar story for Glasgow as the club have never reached the knockout stages of the pan-European tournament.
This season's adventure is rounded off with a trip to Exeter Chiefs on Saturday before welcoming Top 14 giants and current champions Toulon to Scotstoun.
And despite having little less than pride to play for Townsend is urging his Warriors to finish their European campaign on a high.
"We know that over the last two Heineken Cup games we are playing for pride in European terms," Townsend told the Glasgow Evening Times.
"But we also have a great chance to show that if we produce our best form we are capable of matching any side in Europe.
"We went down to Sandy Park in pre-season and got a win there, and while you can't for one minute compare a friendly game with a Heineken Cup tie, at least the players are familiar with the venue and have also had a look at the Exeter squad in their environment.
"On top of that, we produced one of our best performances of the season to beat them at Scotstoun, in the first Heineken Cup tie with them. And if we could back that up by winning at Exeter it would provide a huge boost.
"Then it is the European champions Toulon coming to Scotstoun and we will be determined to go out on a high at home in front of our support.
"So we have two fantastic European games awaiting us in the next fortnight, and although we would have preferred to be going into them with qualification still a possibility, they are still massively important to us in terms of the knock-on effect for the rest of the season."
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