"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," Houllier told his clubs official website.
"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."