Murphy, who has been named an ERC Dream Team member, hailed the quality of the European competition, which begins in just over a week.
"The Heineken Cup is a tremendous competition", said Murphy.
"I've been very lucky to win it a couple of times and unlucky to lose it a couple of times. The losses are probably more memorable than the wins because they hurt so much.
"I have a bit of experience in the Heineken Cup. I've been around for a while and I would love for some of the younger guys to get a Heineken Cup medal.
"It's an amazing experience that you keep with you for the rest of your life and it's something which I am incredibly proud of.
"We have some world-class players and we can compete against anyone. But we have a very difficult group so we have to get out of that first. We have to concentrate on one game at a time and take points when we can."
First up for the Tigers is a trip to Italy to face Benetton Treviso, before a home tie against the Scarlets and a mouth-watering double header with French giants Perpignan.
But for now at least, the Round 1 trip to a Treviso side who have started life in the Magners League with a bang is the only encounter on Murphy's mind.
"We have to go to Treviso and it's going to be very difficult," added Murphy.
"They've had a lot of money pumped into them and they're playing really good rugby.
"They've beaten Leinster and the Scarlets, and only narrowly got beaten by Cardiff Blues. So we will have our work cut out and it will be very difficult opener for us."