It is looking increasingly likely that 4th place will be decided on the final day of the season at Anfield in the showdown with the Geordies.
Houllier believes that his side will have the mental strength to hold onto fourth spot as their Old Trafford triumph showed.
He said: "With the injuries we've had and the flak we have taken it is a mark of our character that we are still chasing fourth place with only three games to go. Now we need to show that until the finish.
"We had a meeting the day before the United game which I think will prove important for the rest of the season.
"We were in control at Old Traf-ford, apart from a ten minute spell in the second half. We never panicked and we were never over-whelmed when they tried to put us under pres-sure. They didn't hurt us enough.
"We have showed in winning at Chelsea and now Manchester United that we can compete with the best but this season has been very strange and very tough. It has been difficult.
"At times we have had more players injured than available, but with four games left we have everyone available and it can make a difference."