English double-winners Leicester do not have things much easier after being pitched with three-times champions Toulouse, Irish top seeds Leinster and Edinburgh.
The two pools will throw up some thunderous encounters but only the group winners and the two best-placed runners-up will qualify for the quarter-finals - so the tournament is guaranteed to lose big names early.
Even qualifying from second place will be tough for Wasps given the competitiveness of the group and McGeechan knows how important it will be to pick up points on the road.
"We have certainly been drawn in a very competitive group, which promises some tasty games and big challenges for us in the pool stages," he said.
"To qualify, we will need to perform on the road as well as at home, as I think good away performances can be the determining factor in any team's chances of qualification.
"I think we came of age when we won in Castres last season to qualify for the quarters, and that helped us a lot in the knockout stages of the competition."
Bristol's reward for an outstanding third-place finish in the Guinness Premiership last season is to be drawn in pool three against French champions Stade Francais, Cardiff and Harlequins.
Bristol boss Richard Hill said: "We're not expecting to win the tournament this year. What we wanted was a group where we could get a couple of wins and put in a creditable performance.
"We've spent the past two seasons establishing ourselves in the Guinness Premiership and now we want to spend the next few years doing likewise in the Heineken Cup so that we can compete with the Leicesters and Wasps of this world."
Celtic League champions the Ospreys are the top seeds in pool two, which also features beaten Premiership finalists Gloucester, Bourgoin and Ulster.
Gloucester boss Dean Ryan insisted "this is a tough draw for us" but was relieved to have avoided the more difficult groups.
Ulster's director of coaching Mark McCall added: "This is a group I firmly believe we can get out of."