The Reds boss said he felt the shock 3-2 FA Cup fourth-round defeat to Oldham highlighted the need for further depth to be added to his set-up.
Rodgers has brought in Daniel Sturridge for £12m and Brazilian playmaker Philippe Coutinho is expected to complete his move shortly from Internazionale.
Liverpool will be hoping to bounce back to winning ways in north London against Arsenal at the Emirates in the Premier League on Wednesday night and Rodgers said: "Yesterday highlighted that when we do change the team around, we don't quite have that bit of depth yet.
"It was another marker in the fact that we want to develop and improve the group, and that's something that I'm sure we'll do over the coming windows.
"There's no number on it but we'll see what we can do before Thursday. If we don't get everything done that we would want - which we won't do, that's the reality - I have always said that it's going to take a few windows for us to get the squad competitive.
"If we can add another player, if not more, then great. If not, we'll look in the summer to keep the building process going."
Meanwhile, asked about the possibility of the Uruguayan defender Sebastian Coates leaving the club on loan, the manager said: "We haven't had any approaches.
"There's obviously lots of speculation and lots of rumours but so far we haven't had anything through from any club.
"I have said in the last couple of weeks that he is a player who I believe needs games and needs to go and play but obviously, I need to protect the club as well in relation to the size of the group.
"Everyone knows how small we are as a squad. It might be the best thing for Seba to go on loan, but it might not necessarily be the best thing for the club.
"There's still a few more days to go, so we'll assess that and take it from there."