Having last week lost out on primary target Mohamed Salah to Chelsea after the Stamford Bridge club came up with a better financial package, Rodgers admits he is struggling to find suitable alternatives at the right price.
Injuries are currently denying him the services of defenders Glen Johnson, Daniel Agger, Jose Enrique and Mamadou Sakho as well as midfielder Lucas Leiva, with Joe Allen still not 100 per cent fit but possibly in contention for Tuesday's 222nd Merseyside derby.
The Reds boss knows his squad are stretched but hopes to be able to muddle through for a couple of weeks until some of his injured players return.
"Of course I wanted to strengthen the team that was already here, and if I couldn't do that it would be disappointing," he said.
"We will see where we are once the window shuts. If we don't get them in then as coach I work with what I got.
"My sole intention would be to maximise everything we have left and I will rinse everything out of the players I have available.
"I said to the players in a meeting the other day we have to fight in these remaining games and for the injured ones to get back as quick as they possibly can because we are going to need every one of them.
"If they are not, we have to find ways to win games and we have to remain optimistic until they all get back.
"I have tried to build something here which means we are not overly reliant on one player.
"We have shown we can really challenge at the top end and we have wanted to bring in a few players of quality that could help us and let's hope we can do that between now and the end of the window."
The Salah deal broke down because Liverpool were not prepared to go above their valuation for a player and Chelsea stepped in with a better offer to the Egypt international's Swiss club Basle.
A player's value is an arbitrary factor and Rodgers admitted if other sides were prepared to pay more that was something he could do little about.
"That is something which is out of my control," he said.
"We can identify the players we want to bring in and hope we can get them in, and the club will do everything we feel possible to match the value and worth of the players.
"If they end up going to another club of course it is difficult to take, but you can't worry too much about it.
"The money guys will decide that: the construction of the whole deal with not only the whole player but the agent and the football club.
"It was deemed in this case we couldn't do a deal and Chelsea could and the boy went there."
Anfield is a venue where Everton have not won since 1999, but in the last two seasons the Toffees have finished above their near-neighbours in the league.
Rodgers rejected the suggestion Liverpool should always out-perform their city rivals purely because of their better financial position.
"Whether it is wealth or not that would not matter to me," he said.
"It is easier said than done. Everton for the last two years have finished above us.
"They have had consistency and stability there as a club but, irrespective of wealth, we would see ourselves up there as a club challenging."
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