"We've got two wins from two and we're reasonably happy with that," said Murphy, who played in both Leicester's previous Heineken Cup triumphs and toured with the Lions in 2005.
"Treviso played very well. They tackled their hearts out and we only pulled away in the last 20 minutes."
The win sees the Tigers top Pool 3 with nine points from a possible 10 ahead of back-to-back games against French side Perpignan in December.
"We played a lot of good rugby in the first half against the Ospreys but we didn't take our chances," said the 30-year-old Irishman who, alongside Julian White, Ben Kay and Martin Corry, was one of four Lions in the Leicester starting line up.
"We still missed a few today but we showed a marked improvement in terms of our finishing.
"It would have been nice to get a bonus point last week, or at least have prevented the Ospreys from getting one, but we're out of the blocks now, although we've got two tough games with Perpignan coming up next."