Houllier believes Jerzy Dudek's blunder, which gave Tottenham a 49th minute lead, helped Liverpool focus on the task confronting them.
Houllier said: "Maybe Jerzy's mistake woke us up! The team wanted to respond to help him out and the seond half was full of energy. I must praise the players for the team solidity, especially after the Celtic game.
"We rode our luck at times in the first half but did very well in the second half. I felt we could achieve something today, this is actually my first ever win here as Liverpool manager and it was a very good and vital win.
"There is eight games left to play and all the games are cup finals. I like the character of my players today to come back from one goal down away from home.
"We got the ball on the ground and played some decent football in the second half and we defended well. Djimi Traore is maturing into a good centre half."
Click here to listen to Houllier's post-match interview