The England international has been ruled out for up to two months with ankle ligament damage that he suffered in training on Friday, leaving just Luis Suarez and the relatively untested Iago Aspas as the Reds' only striking options.
"I think every window for us will be exactly the same - if there's a player we think can improve our squad and in particular the team, I'm sure we will be able to go out and get that player," Rodgers told the press.
"It was always going to be the case that if we had a few injuries to key players, that leaves us light.
"It's no different to a lot of squads, but for us it's even more prominent because Daniel Sturridge and young [Philippe] Coutinho were not playing and they are good players."
Liverpool host Norwich City in their next match on Wednesday.