"We conceded a goal and then we conceded another goal, which to me was offside, the second goal," he said.
"I think the second half started extremely well. Everybody would have expected we would score a goal. We had a good chance with Gabi [Agbonlahor] but unfortunately on the back of that we conceded a third goal so it was game over.
"[But] I cannot fault the players for the effort, they tried hard. When you concede a goal after 13 minutes at Anfield it's hard to come back. It's a shame because we could have done something here. We are not the most confident team at the moment and we are aware of that," he added.
Houllier also refused to use injuries and illness to key players as an excuse for the poor performance.
"I don't think things will improve if you start moaning about injuries and sickness. We rushed Marc Albrighton back after an appendicitis operation two weeks ago and last night Gabi [Agbonlahor] was sick and we didn't know until this morning whether he would be playing or not.
"[But] this for me is not a way to progress - to look for excuses or blame others," he said.
With the Premier League table still very congested, Houllier feels it would not take much to change Villa's fortunes.
"Two or three wins and we would be back in the top half of the table but we need to concentrate on the fact that there are a few errors in our game which can be improved and one of those is the need to defend better," said Houllier.
Liverpool manager Roy Hodgson also had to make late changes after Fernando Torres missed the match to attend the birth of his second child, a son.
Hodgson hails 'important' win over Aston Villa
"I certainly wasn't planning for it. I knew Fernando's wife was very close to giving birth," added Hodgson.
"I was hoping it wouldn't be yesterday, I was hoping it would be Sunday or the day before or a couple of days after but this is what happens.
"It's called Sod's Law that it happens on the very day you need him but luckily we've survived comfortably without him."
Hodgson also praised Dutch midfielder Ryan Babel who marked his first Premier League start of the season with a goal.
Babel was reportedly close to leaving Merseyside in the summer but he set up Milan Jovanovic's goal in the 1-1 draw at Steaua Bucharest last week and kept his place against Villa when Torres pulled out.
"I've never written Ryan Babel off," said Hodgson. "His chances have been limited because we have Torres, David Ngog and Steven Gerrard so the competition is fierce."
"But I'd never written him off and I have also accepted his claim that he prefers and is better playing centrally than being forced to play wide.
"We've worked on training with him in those positions and he did well at Steaua Bucharest.
"When Fernando was unable to play I had no hesitation in putting him [Babel] in the team because by doing that I could keep the same shape as in recent weeks and it's a shape which I think is serving the club well."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.