Three defeats and a draw is all they have managed at their normal "Welford Fortress" in the English Premiership but now the clash of two former European champions, Ulster Rugby winning in 1999 and the Tigers in 2001 and 2002, is a must win contest for Geordan Murphy's team.
"We need to win next week at Welford Road - you have to keep winning in this competition," said Director of Rugby Richard Cockerill. "But Ulster are a good side with some very good individual players so it is a massive game.
"These are the deciding games of the season and if we come away with two from two and with eight or nine points then that will be a huge plus.
"We hope to have Billy Twelvetrees and Ben Youngs available for selection, but how much they will be involved remains to be seen, although the positive is there are no further injuries.
"The 28-12 result against Aironi in Monza was an important away win, which is tough to get in Europe. The Heineken Cup is very difficult and there's a long way to go and you have to take the win and take the positives."
Tigers captain Murphy - who could be in line to announce his retirement from Test rugby - added: "Ulster are a good side and picked up a couple of away wins last year.
"They will fancy coming to Welford Road. They've made some really good signings over the last couple of years with guys like Ruan Pienaar, Pedrie Wannenburg and John Afoa.
"There is a lot of talk about their South Africa core but they have some very good young Irish players as well - Ian Humphreys, Steve Ferris, Andrew Trimble and Paddy Wallace - the latter so underrated and a player I really respect.
"I'm pleased to get a good win as Aironi are a tough side. We watched a lot of footage of them building up to the clash and they took this match to a big stadium and wanted to put on a show - it was a cup final for them.
"It would have been nice to get the bonus point, and it was really frustrating to get the third try on 80 minutes. We should have got more out of the game, but full credit to Aironi they defended well and were aggressive.
"There is a long way to go and we might have to pick up bonus-points later in the season but hopefully it won't come back to haunt us.
"Now it will be interesting to see what happens - and that's the interesting thing about the Heineken Cup, there are so many permutations. Aironi are a very good side that work hard and deserve a lot of credit. Hopefully they can help us out and get a scalp later in the competition."