"It's a shame. Even a draw would have been a great result after what happened in the game.
"I'm disappointed with the result, but happy with reaction of players. Credit goes to them, in terms of what they put in the game.
"Their effort was good - and I liked their character and temperament, because they did everything they could to equalise. We've got senior players who know where we are and how important the points will be in future games."
Houllier also insisted he retains the backing of club owner Randy Lerner and chief executive Paul Faulkner.
"I spoke to Paul Faulkner and he was very supportive," the Villa manager added. "I don't doubt Randy Lerner's firm support and determination. We are in this together for better or worse."
Sunderland manager Steve Bruce felt that victory came at a price in terms of injury setbacks - and blamed himself for the season-ending injury picked up by David Meyler.
Injuries mar victory for Bruce
The 21-year-old midfielder, who had only just returned from eight months out, suffered cruciate knee ligament damage and will be out of action for at least another six months, while on-loan Manchester United striker Danny Welbeck suffered a hamstring injury.
"Meyler looks as if he has ruptured his cruciate knee ligament which is the same one as before," said Bruce. "We are devastated.
"He was magnificent on Saturday against Blackburn and I'm kicking myself now because I've played him. Whether it is because he was tired, I don't know.
"Basically we didn't have anyone else.
"Always in the back of your mind is that he played his first 90 minutes then and I asked him to play again two or three days later when he has been out for eight months.
"In the Premier League you get players having to play five games in 13 days and players are picking up injuries through fatigue," Bruce added.
"It was a tremendous victory, but we have now got 10 players missing and we may have to bring one or two bodies in during January."
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