It has been four years since Wasps stormed Europe to become the last representative from the Aviva Premiership to seize the most coveted prize in northern hemisphere rugby.
But Northampton reached this year's final and were on course to upset champions Leinster before running out of steam in the second half.
Brown, who is currently participating in the Churchill Cup with England Saxons, takes heart from Saints' progress.
"I believe an English club can go on and win it. Northampton were really close," he said.
"It's about turning up on the day and playing to the best of your ability.
"Any club from England in this competition is capable of winning it."
French clubs benefit from a far higher salary cap while the Irish provinces plan their entire seasons around the Heineken Cup knowing they can rest players for Magners League matches.
However, the Premiership supply seven teams to this year's competition, the most of any nation, so should be represented in the knockout stages.
Two English clubs have been drawn in the same group with Harlequins and Gloucester battling it out with Toulouse and Connacht in Pool 6.
Brown believes that Quins' Amlin Cup triumph this season will prove ideal preparation for Europe's greatest stage.
"Winning the Amlin Cup will give the lads a boost and it is good to have got that silverware under our belts," he said.
"Playing against Heineken Cup teams that have dropped into the Amlin Cup will hold us in good stead for when we play Toulouse and teams like that."
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