McIntosh and co haven't tasted victory in the league since success against Newport Gwent Dragons on New Year's Day and few outside of the camp expect them to buck that trend against a travelling team who eased to victory in the reverse tie in October and have won all five league fixtures in 2014.
But McIntosh, who took over the caretaking coaching duties alongside Paul John following Phil Davies' resignation earlier this month, knows that his side are capable of beating even the very best, but only if they show the kind of self-belief that was lacking at the Liberty Stadium.
"People don't expect us to beat Ulster. I do and I hope the players do," said McIntosh, whose team sit 10th in the RaboDirect PRO12 table with five games left to play.
"Ulster are an unbelievable side with a matching culture and they've got some exceptional rugby players. They've got a great balance of youth and experience and they are very well coached. It's a huge challenge.
"We're down on confidence, we struggled on Friday night to play with any kind of passion which meant we weren't going to win. We all have bad days but a very good side will bring those players through a tough game. It's all about belief and we lacked that last Friday. The players didn't believe that we could win."
McIntosh has been as brutally honest as ever in his assessment of what went wrong in Swansea, with the former Wales back rower admitting that the squad let the region and their people down in one of the most hotly-anticipated games of the year.
Passion has never been a problem for the ex-Pontypridd star but he refuses to shy away from the fact that the nature of the result and performance last time out has left him and his players feeling wounded this week.
"We've done an injustice to the jersey and all the criticism we have had is totally just. I'm hurt by (former Wales and Blues flanker) Martyn Williams' comments after the game, saying it was the worst performance of the season, because he's a great friend of mine," added McIntosh.
"I felt like I'd let him down because he's been such an ambassador for this club. We used his name in the build up to the game as a motivational tool and I'm gutted that we've done the jersey an injustice.
"The assessment of the game has been volatile. Paul John and myself speak from the heart, that's just how we are. We understand the expectation on that jersey and we've let a lot of people down. It was about soul searching after the game and making the players understand that it's not acceptable to perform in that way.
"We represent two cultures: Cardiff, the city of opportunity, the biggest city in Wales, and the Valleys, which represent hardship and negativity. Those two cultures combined should be a dangerous animal, but at the moment it's not.
"Our defensive problems last Friday weren't systematic, they were down to individuals going out of the system which meant they scored some pretty soft tries. We were under a lot of pressure because we kept giving away turnover after turnover. Eventually we leaked. I can live with that when we run out of steam but I can't live with individuals letting people down, especially when we have hammered our strategy home all week.
"We've touched upon that this week. We named and shamed as we do - people might not think that's professional, but that's life. When you do wrong you need to know about it. Hopefully those players will not do that again."
Judgement Day returns... The Millennium Stadium is set for another double-derby extravaganza on Easter Sunday 2014 with the Cardiff Blues taking on the Scarlets at 2pm and Newport Gwent Dragons facing the Ospreys at 4.45pm. Tickets are available from wru.co.uk/tickets or from all four regions.