Ulster and Cardiff both lost their opening round Pool 6 matches, Cardiff going down at home to Biarritz Olympique and Ulster away to 2000 Heineken Cup winners Northampton Saints.
"We are in a very tough group and, to stand any chance of progressing to the knock-out stages we will have to win all our home games and then look to pick up a win or two away from Belfast," said Solomons."Northampton were a very powerful outfit and you could see from the game between Cardiff and Biarritz just how good a side the French champions are."
Even though he is named in the starting line-up, Ulster are sweating on the fitness of fly half David Humphreys, who failed to go the distance at Northampton with a left knee injury, while the issue of the captaincy is also something of a hot potato.
"The captaincy of Ulster is a bit like a poisoned chalice at the moment - every guy who takes it over seems to get injured," said the coach. "First there was Andy Ward, then Jeremy Davidson and now David - and even when Jonathan Bell took over from David on Sunday he limped off with a dead leg.""And, as a team, what we have all realised is that the pace of the game in the Heineken Cup is a lot quicker than in the Celtic League. There is a substantial step up from the rugby we have been playing so far this season.""Having a Sunday match and then playing on the following Friday has put the pressure on us because it does not give the players much time to recover."
And as far as Cardiff coach David Young is concerned, his side needs to be much more disciplined in Belfast.
"We keep letting ourselves down a little bit with yellow cards and it may be something we need to address," said the former Lions and Wales prop.
Ulster. Bryn Cunningham; James Topping, Shane Stewart, Jonathon Bell, Tyrone Howe; David Humphreys, Neil Doak; Justin Fitzpatrick, Matt Sexton, Rob Kempson; Gary Longwell, Jeremy Davidson (capt); Warren Brosnihan, Neil McMillan, Tony McWhirter.Replacements: Simon Best, Paul Shields, Mark Blair, Neil Best, Kieran Campbell, Adam Larkin, Scott Young.