Ciaran Clark scored twice for Villa to give them hope but the Gunners eventually won 4-2 in a thrilling encounter.
Houllier said: "We were poor in the first half. Whether it was because we showed them too much respect, or lacked experience, I don't know.
"We never got started. We were a different team in the second half, showed more energy and took more risks.
"It's just a shame that when we got to 2-1 that we couldn't keep the score like that for 10 minutes because, after what happened to Arsenal last week, they would have been shaky.
"Their third goal was the pivotal moment of the game but overall we were beaten by a better team than ourselves, simple as that. The best thing to do as a team is to learn from that and the good thing is we did get a positive reaction in the second half."