Liverpool completed the signing of Dejan Lovren from Southampton ahead of their 1-0 friendly win over Olympiakos, as part of the club's preseason tour of the U.S., to take Rodgers' summer spending close to the 100 million pound mark.
But after missing out on QPR's Remy and seeing Lallana suffer an injury in training, Rodgers insisted he will not panic buy.
"There is money to spend, no question, but I won't spend it for the sake of it. It has to be the right type," he said. "If that means I have to wait until January then that's what I will do. The players at the moment are in great condition. They are working very well and very hard.
"I have seen the development in some of the young players but if the right ones become available we would like to do something because I still have a lot to do on that front -- but if they're not available, I will wait."
Summer transfer window roundup
- Premier League: Team-by-team ins and outs
- Transfer Centre: All the done deals
- Marcotti: Mind-boggling transfers
- Delaney: What did we learn on deadline day?
- Horncastle: European transfer grades
- Smith: Transfers more important than the game?
- Macintosh: We worship goals, not balance sheets
Of the Remy deal, Rodgers said: "It's very simple -- we've made a decision as a club not to go ahead with the deal. It's unfortunate for the player. We're disappointed for the player but there's nothing more to be said and we will move on and look at other targets."
Lallana, who damaged his collateral knee ligaments in training, does not need surgery and will remain in the United States in order to get to know his teammates.
Rodgers added: "Last year if someone like Adam had gone down it would have really hurt us. It's unfortunate for him but thankfully at this stage of the season, where he has got a good level of fitness, it means he can recover quicker.
"He won't be too far away after the start of the season, which is great news. This year is vital for us. You're going to pick up injuries and we need to have the players who can step in and that's what we are trying to build."
Raheem Sterling's fifth-minute goal was enough to see off Greek champions Olympiakos at Chicago Fire's Soldier Field stadium. Sterling tapped in after Daniel Sturridge's scuffed shot fell kindly for the England winger.
Rodgers said he was "delighted" with his new-look attack, particularly Sturridge, Sterling and the lively Lazar Markovic, as Liverpool continue with life after Luis Suarez, who left to join Barcelona for 75 million pounds.
"We will get sharper but at the minute we are building up the resistance," he said. "Our passing was crisp and precise and I was also pleased with how we defended. Overall I was delighted.
"Markovic looked exciting and Sterling was a joy to watch. I have seen a difference in Daniel and I think he's ready to be the main man. He has come back from the World Cup looking really sharp."