Manager Houllier brought on Emile Heskey and Stewart Downing and both responded with a goal to earn his side a 2-1 success over the Clarets at Villa Park after extra-time.
Heskey looked to have won the tie in normal time before Clarke Carlisle's last gasp equaliser but then Downing's stunning strike sealed a last eight place.
Houllier said: "I don't take credit for the subs. The manager makes the decision to bring them on - but it's down to them.
"They scored the goals, I didn't. I wanted to rest some players but I knew at some stage, with other players tiring, they would make a difference.
"Emile made a difference and Stewart made a difference.
"The problem with the subs is they have got to be in the right frame of mind.
"If they have the right attitude, if the hunger is there, then they bring something.
"Their freshness can bring initiative which was the case. Emile came on and changed the game because he held the ball up."
Villa ended the game with 10 men after winger Marc Albrighton was red carded for a professional foul on Burnley sub Wade Elliott and he will be suspended for Sunday's derby with Birmingham.
Houllier said: "To me, Albrighton's sending off was a fair decision.
"He didn't touch him (Elliott) a lot but he touched him and the player used it as if he had been shot dead - but he touched him.
"From Marc's point of view, he should have reacted quicker. This is one of the main progresses we have to do.
"You need sometimes to have game awareness and next time he will understand that."