"You've got to be strong enough to take it on the chin and go on," added Houllier. "In that particular circumstance the referee had whistled and it was a free-kick so we should get on with it."
Asked about the overall game, which lacked quality, he stated: "We could have done better, maybe it's because it is a derby, extremely tense, very tight, competitive, both teams were extremely committed to the job but didn't allow many chances.
"It's a derby and sometimes they are not allowed to play. Credit to Birmingham they had a clean match, it was physical but not over the top and the referee held the two teams very well."
Houllier also pointed to the gruelling extra-time victory over Burnley in the Carling Cup on Wednesday and said: "We lacked a bit of freshness after the two hours of football in midweek. The introduction of some players brought more invention to our game and more creativity which we need."
The former Liverpool boss was encouraged by the efforts of striker Emile Heskey, who he managed at Anfield, and believes he can continue to play a useful role at Villa Park into next season.
"I think so. It's a matter of faith and belief, but he works extremely hard for the team, he did his job, had a couple of half chances but his work is more for the team," said Houllier.
Birmingham manager Alex McLeish was relieved to end a run of six successive defeats against their local rivals but felt his team could have taken all three points.
McLeish pleased with Blues display
"At last a crumb of comfort but I thought it was a well-deserved point," stated the former Rangers boss. "We were exceptional organisation-wise, the defenders were on top of their game, we did well in midfield and started to look quite dangerous when [Alex] Hleb came up a gear.
"I thought we had probably the best chances of the entire match, Villa had a near miss near the end but it's one of our best performances of the season."
Indeed substitute Cameron Jerome might have won it for Blues but failed to make the most of a good opening in the latter stages.
"It was a great run in the channel, he just had to calm down a little bit, if he had passed it earlier with that bit of relaxation that he is trying to improve on, he would have had big [Nikola] Zigic in for an easy tap-in."
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