Baros suffered a broken ankle following a tackle from Markus Babbel while Bootle-born Carragher was the victim of a horrendous challenge from Lucas Neill that broke his leg.
Neither player will be in action for the Reds again this year and Houllier insists that the traumatic events of a frenetic first half at Ewood Park was motivation enough for his team.
Houllier said: "I told the boys at half time that we had to win it for Jamie and Milan. We kept our heads up and kept going. We didn't want one point, we wanted three.
"I've got mixed feelings. Our victory was soured because, although we won, we've got two injured players.
"It was a dramatic start to the game and we knew we just had to pass the ball and be patient. We played very well and deserved our victory. I'm pleased we kept our heads up and kept going. I thought Vladimir Smicer was brilliant. It's the third consecutive game we have played well."
