Their achievements show the club have come a long, long way from when Hastings himself played in his only full season in the continent's top competition back in 1996/97.
Michael Bradley's men have already beaten London Irish and Racing Metro home and away and Cardiff Blues and Toulouse on Scottish soil whereas Edinburgh's first foray into the Heineken Cup saw them suffer successive losses to Bath, Pontypridd, Dax and Benetton Treviso.
"In 1996 it was a step into the European unknown," Hastings told The Scotsman at the launch of the Glasgow leg of the HSBC World Sevens Series.
"Sport moves on but back then it was literally a case of getting on the bus after a couple of training sessions and seeing where it takes us.
"At that time we were representing Edinburgh and also our clubs week in, week out. It was only by having extra sessions that we were able to put in a game plan to go to Bath against the likes of Andy Robinson, Matt Perry, Jeremy Guscott and Jason Robinson.
"We were staring down a barrel, facing a 70 or 80-point hiding. We came back, scored a couple of tries and realised that with a bit more effort we could compete. (Edinburgh lost 55-26 to Bath at The Rec in their first Heineken Cup fixture).
"The team are now only 80 minutes away from a Heineken Cup Final and who would have forseen that at the start of this season?"
Hastings also believes Edinburgh's Heineken Cup heroics have proved that Scottish fans will turn out in their droves if a successful product is on offer at either of the nation's two professional sides.
The quarter-final win over Toulouse was watched by a crowd of just under 38,000 - a record number for a Scottish professional club game - and the ex-British & Irish Lions centre is convinced this could be the start of something special for both Edinburgh and RaboDirect PRO12 play-off hopefuls Glasgow Warriors.
"Edinburgh's efforts in beating London Irish and Racing Metro home and away in Europe as well as Toulouse shows that pro rugby can engender great support, atmosphere and loyalty," added Hastings.
"It has taken Edinburgh too many years to be able to compete on a regular and consistent basis but, now that they have, the manner and style of dynamic rugby they play has ultimately made for a fantastic support.
"I came back from the Rugby World Cup and said there was a lot of wrongs to be put right by the Scottish players. They have not been able to do it at international level but what I have seen in Glasgow and Edinburgh is a belief to be able to compete in domestic and European competition."