"It was tough going," said Murphy, who played his part in both Leicester's previous European triumphs in 2001 and 2002.
"I thought we were very disjointed and were well below par but it was good to get a five pointer at home.
"It's important to play well but you could play well and not end up with a five pointer. You have to take the fact that we didn't play to our potential and still got five points."
The win means Leicester now top pool 3 by five points having recorded three victories from three attempts so far in the competition. Next up is a trip to France, however, and Murphy knows the Tigers will not get an easy ride.
"It will be a lot tougher next week down in Perpignan so we'll definitely have to step up our game for that.
"There will be more intensity and they'll raise their game at home. Cocker (forwards coach Richard Cockerill) has played down there and he's told us how tough it's going to be and I've played there before and we've lost.
"I think certain French clubs are very difficult places to go and Perpignan is one of the toughest. They're a strong side and there will be a partisan home crowd getting behind the team so it'll be tough going.
"The guys with a little more experience need to lead from the front. We'll have to match them physically and tidy up our game and not make as many mistakes as we did tonight."
Despite reaching their fourth Heineken Cup Final in 2007, Leicester's European dream ended at the group stages last season and Murphy is determined to ensure his side don't suffer the same fate this time around.
"It hurts a lot when you get knocked out of this competition.
"I think every team wants to do well in it and when we don't do well, it's very disappointing. It's important to get out of the group first and foremost and then the competition really starts."