Javier Mascherano and Daniel Agger will not feature against Trabzonspor on Thursday night after picking up injuries against Arsenal.
Mascherano sustained a pull in his calf while Agger is still suffering from concussion after a ball to the face which has left him with no recollection of Sunday's clash.
Both players now face a race against time to be fit for Monday's match at Manchester City.
Asked by reporters whether Mascherano was in his plans for the Europa League play-off, Roy Hodgson said: "Javier will always be in my plans until the day comes when he leaves the club. And for me that will be a long time in the future if I can get my wish. But he's injured at the moment and won't play tomorrow.
"He came off after about 80 minutes on Sunday with a slight pull in his calf muscles and has only just started to jog today.
"The worry for us is that he won't be fit for Monday.
"Daniel got concussed so he's not doing that well. We're three days after the incident and he's still suffering from concussion and has got no memory of the game.
"We can only hope that it settles down in time for Monday's match with Manchester City. There was never any question he'd be fit for tomorrow.
"He is resting. He was at the club this morning, I was talking to him, but he's not able to do much at the moment because he's suffering from headaches. Even something as simple as reading a newspaper or watching TV can give him a headache so he needs to take it easy. I know how he feels doing all these press conferences!"
Mascherano's absence could open the door for new boy Christian Poulsen to make his Liverpool bow.
Hodgson added: "He's in the squad. I haven't picked the team yet but he's in the squad and there's a chance he'll appear tomorrow.
"We'll only find out when he plays if he's fit. He's only played 20-25 minutes in a friendly match for Juventus. He's done a lot of physical training so in that respect he's right up there with the rest of the players but he hasn't played a lot of football and so is not match fit.
"But he's a quality player. He's been at Schalke, Seville, Juventus and now Liverpool. The players here are like the ones he's played with in the past and his quality is Liverpool quality."
Click on the image below to watch the boss talking about the latest injury news
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