Houllier said: "Birmingham are a difficult side to break down and beat and it was a bit ugly out there at times but I don't mind winning ugly as long as we get the three points.
"Birmingham scoring first was a wake-up call and we reacted by equalising straight away. I told the players at half time it wasn't good enough and we had to improve.
"We did well in the second half. Steven Gerrard led by example and our energy and work rate was outstanding. We scored two fantastic goals through Harry and Emile."
The Frenchman was also full of praise for Emile Heskey, who claimed his 100th club goal in spectacular style, but warned his under-fire forward that he must now deliver his undoubtrd potential on a more regular basis.
"The third goal showed the quality Emile has but has to start delivering that on a more regular basis."