Everton's Leighton Baines struck a late penalty to secure a 2-2 draw at Goodison Park after a Darren Bent double looked to have put troubled Villa on course for three valuable Barclays Premier League points.
Houllier, whose side are just two points above the bottom three, said: "It is always difficult to get a point at Everton, it is not an easy place to play. I felt we fought hard enough to get the three points because we came back after making a mistake in the first half. We showed more competitiveness."
He added "I am disappointed with the result because there were eight minutes left when we conceded the penalty.
"But taking into account that morale and confidence is not at its highest, the fact we came back in the second half and won it 2-1, that is what we have to take.
"I would say it is two points lost because we were in a winning position in the game but in terms of attitude, it was a hard-fought point and we deserved that, minimum."
Villa fought back well after a sluggish first half in which Leon Osman opened the scoring after 38 minutes and the visitors felt the 82nd-minute penalty award against Jean Makoun was harsh.
Yet the home side could also feel aggrieved after a Jermaine Beckford shot bounced close to the line after hitting the crossbar just seconds before Bent grabbed his second.
Everton manager David Moyes said: "The angle the ball came back off the bar made me think it must be close. It is a hard call for the referee and the linesman but I thought they would have picked up on the angle of the ball coming off the crossbar.
"It was a double whammy because within 10 seconds were 2-1 down - but that was down to us, not the referee. It was a poor decision - that is why we have been championing for goalline technology."
Source: PA
Source: PA