The Reds played the last 20 minutes of extra time with a man less after using all three substitutes, and Rodgers said that it was a tough night following knocks to Kolo Toure, Joe Allen and Aly Cissokho.
"Kolo Toure, we need to assess it. His groin opened up a wee bit. He overstretched his groin and it doesn't look so good, to be honest," Rodgers told the club's official website.
"Cissokho was devastated; he shouldn't be [out] too long. He's got a knock in his ankle. He was distraught to come off in his first start [at Anfield].
"Joe Allen's may well be a hamstring so we'll have a look at that. We'll know more in the morning but it wasn't a good night injury-wise."
The Reds have won all three of their games so far this season.