The capital side were among the bottom seeds for the competition and landed in Pool Two alongside Guinness Premiership champions Wasps, Magners League champions Leinster and French outfit Castres.
The competition begins in October and the final will take place at Murrayfield next May.
Scotland great and Edinburgh chairman Hastings believes three wins at home will be essential for the Scottish side, which he insists is an achievable target.
He said: "It is going to be tremendous to get the best teams in Europe coming to Murrayfield and I'm really excited about what we can achieve in the Heineken Cup next season.
"Both Wasps and Leinster have been very competitive over the years and I think that augurs well for a real challenge in the Heineken Cup during the forthcoming season.
"But both those teams will realise Edinburgh can be very competitive, particularly in the games at Murrayfield after being on the receiving end of losses over the past few years."
Edinburgh beat Wasps 32-31 in a Murrayfield thriller in October 2005, and former England head coach Robinson's team have beaten Leinster twice at Scotland's national stadium in the past year.
As well as a clean sweep at home, Hastings wants to see Edinburgh pick up points on the road.
"The players know that, if we want to progress, we are going to have to win away from home; it is as simple as that," he said.
"My feeling is that we have to go out there and win all our home games and hopefully get one or two away victories.
"It is the sort of pool where any team can beat any other team, particularly when they have home advantage.
"Wasps and Leinster have both tasted defeat at Murrayfield over recent seasons, so they are not going to take Edinburgh lightly by any means.
"Castres are slightly different in that respect and perhaps an unknown quantity."