Striker Daniel Sturridge suffered a thigh strain on England duty and is expected to miss three weeks, while Emre Can (ankle) and Joe Allen (knee) also picked up injuries in the recent international break.
Defensive trio Martin Skrtel and Jon Flanagan (both knee) and Glen Johnson (thigh) are also sidelined.
But Rodgers bought nine senior players in during the window and is convinced the likes of Mario Balotelli, Adam Lallana, Alberto Moreno and Javier Manquillo can step in.
"We've been unfortunate," Rodgers told the Liverpool Echo.
"Dan had started the season very well. His performance against Tottenham was excellent.
"He didn't score but his pressing, his positional play, his speed, movement and hold up play was first class.
"He will be missed but we've got a long season ahead and the important thing now is to get him physically right.
"This [injuries] is why it was so important to strengthen the squad during the transfer window.
"We have options now and that's key for us. We had a great window in terms of the calibre of players we brought in.
"We signed young players with quality and some with more experience as that's what we needed."
Balotelli – signed from Milan for £16 million – is set to make his Anfield debut for the club against Aston Villa on Saturday, despite illness restricting his involvement this week.
Rodgers said: "Mario has had a bit of a bug that we wanted to make sure he didn't spread around the group.
"But he'll be okay for Saturday. I think he has felt the warmth of the club since he's been here and I'm sure he will look forward to playing at Anfield.
"He isn't the only one. The same goes for the likes of Lazar Markovic and Adam Lallana who will also be involved."
