Houllier's men meet Aston Villa in tonight's Worthington Cup quarter-final on the back of just one Premiership point from a possible 18.
And after their luckless trip to Sunderland on Sunday they have been hit by a further blow with the news that influential midfielder Dietmar Hamann will be sidelined for a fortnight.
But Houllier says his squad's attitude has remained first class through all their setbacks and he expects an imminent change in fortune.
Houllier said: "I know the mental strength of the players and the way they stick together will get us through.
"We are extremely hurt and we felt a lot of pain after the Sunderland defeat because we didn't think we deserved to leave the stadium with nothing.
"I am still trying to find the solution but I have full trust and confidence in my players and their ability to keep faith in themselves."
Tonight's Worthington Cup encounter provides Liverpool with the opportunity to temporarily shunt their Premiership problems to one side.
But Houllier will name his strongest available side and, as well as aiming for another trip to Cardiff, he believes the game offers the ideal opportunity to put things right before the weekend's Merseyside derby showdown.
He added: "We want to win every cup. The game is all about silverware and winning trophies is what the players think of. The good thing about being a successful side is that you are in lots of tournaments and the lads have an opportunity to bounce back.
Hamann will be sidelined with a shin problem which has recurred after he played through pain at the Stadium of Light. But there is better news on Emile Heskey, who will be involved again after an ankle knock.
Houllier added: "I fear that Didi will be out for a couple of weeks and that is a blow because he's a very experienced player."
Meanwhile, Aston Villa manager Graham Taylor has warned his side to beware of the wounded tiger when they take on out-of-sorts Liverpool.
It would appear to be an ideal time for Taylor's side to face Liverpool and breathe some life into their own season which to date has been a major disappointment. With England striker Darius Vassell getting back to his best, Villa look to have conquered their major early season headache of failing to score enough goals.
But Taylor, whose side were beaten 1-0 at home by Liverpool in August, knows that Villa will have to be at their best to stand a realistic chance of progressing into the semi-finals.
Taylor said: "That wounded tiger mentality does spring to mind in the sense that they could now be at their most dangerous, in looking to put recent results behind them.
Taylor will always have some empathy with Houllier, after his heart problems, following his own much publicised serious throat disorder three years' ago.
That led Taylor having a six week break from managing Watford but it has not reduced his level of passion and commitment for the game he returned to 10 months' ago for a second spell with Villa.
He said: "It's well known that I might have been a couple of hours away from not being here when my wind-pipe was closing up if I hadn't have had the treatment and the drugs I had at the time, although I was not operated on.
"When you are strapped in the ambulance and the surgeon is there with his bag of tricks you aren't thinking where Watford are in the First Division."
Taylor will again be without midfielder Ian Taylor (thigh) while defender Ronny Johnsen is a slight doubt as he is suffering with a virus.
But Steve Staunton is set to skipper the side despite his sending-off on Saturday for elbowing West Brom striker Danny Dichio.