"We'll be trying to build a little bit of form and then take that into Europe," said Murphy, a Heineken Cup winner back in 2001 and in 2002.
"Europe's a tremendously difficult competition to win, as was proved last season.
"I think all the English teams would have been disappointed with their performances last season and we were particularly disappointed with our own efforts."
The Tigers will be looking to improve on last season's continental showing when they were beaten to a quarter-final spot by Magners League winners-in-waiting the Ospreys and soon-to-be-crowned French Champions Clermont Auvergne.
Murphy and his men are determined to end an eight-year drought at Europe's top table but the Ireland full back says his side cannot look any further ahead than the opening pool matches against Benetton Treviso and the Scarlets.
"You can't worry about what's going to happen at the end of the season," added Murphy.
"You have to play it one game at a time and that's how we've done it in the past. It's such a competitive competition that you haven't got the luxury of worrying about who you're playing in three weeks time.
"We're aspiring to win it. First and foremost, we've got to play some quality rugby in the group stages, try and eek a few wins out and hopefully get out of the group. We'll re-evaluate then."
The Tigers have begun the season without a number of high-profile players, many of whom have lifted Europe's greatest prize or appeared in at least one Heineken Cup Final.
But while players of the stature of England captain Lewis Moody have moved to new clubs and others such as Ben Kay have called time on an illustrious career, Murphy insists that the Welford Road outfit aren't looking for excuses in the lead up to their Pool 5 campaign.
"Over the past few years we've lost a lot of big players. We've lost Martin Johnson, Neil Back we've lost Cockers (Richard Cockerill), we've now lost Lewis. The nature of the game is that players move on, that's just the way it is.
"It's not ideal when you have close friendships with people like Lewis Moody, Brett Deacon, Same Vesty, Aaron Mauger who's retired, Hazza Ellis who's retired, Ben Kay who's retired, but the game moves on.
"There's no point making excuses. We've always lost players. We've lost players to international call ups and it's instilled in us from the coaches that you never moan. You take your beatings on the chin and you try and get a win the following week.
"We've got fantastic players in and they can do a good job for Leicester."
Murphy and co start their latest European challenge in Italy on Saturday, October 9 before welcoming the 2007 semi-final opponents the Scarlets to the East Midlands a week later.
Also in Pool 5 are French Championship runners up ASM Perpignan, a side Leicester met in the group stages of the 2008/09 tournament.