Ulster's victory over Connacht ended a run of five defeats in a row after a difficult run of form.
That run included two heavy losses in Europe at the hands of Toulouse and Bordeaux.
Leicester lost their European opener to Bordeaux before bouncing back with a big win over South African side Sharks.
The Welford Road side are fourth in the Premiership with six wins in 10 matches.
Murphy admitted: "We're going there and nobody probably gives us a chance.
"If we want to stay in the competition we need to win our last two games.
"Leicester is a very difficult place to go. They have a massive pack and set piece, and their big back three are all very talented in the air.
"There is a massive test coming in regards to that but we are going there with confidence.
"We want to try and put our game out in front of them and see where we get to."