The French tactician has come in for some criticism this season after he replaced Martin O'Neill at the helm in September as Villa have slipped down the table to within a point of the relegation places following Tuesday's dismal 4-0 mauling at Manchester City.
And Houllier, who has seen his side heavily depleted by injuries since his arrival, feels that Villa are not far off fighting it out at the right end of the Premier League table. But with defeats against Tottenham and City over the festive period, his main focus at the moment is on pulling away from the danger zone.
"Before this game, another three points, which we could have got against Fulham or Manchester United, would have put us in the top half," said Houllier.
"But I told the players they also have to look the other way. There is a drop zone behind and we are very near. We are in a dogfight for that. We have to acknowledge that."