Deals for at least two players have fallen through, with Fulham goalkeeper David Stockdale and former Chelsea and Barcelona striker Eidur Gudjohnsen not expected to follow through on proposed moves to the Liberty Stadium.
"I'm certainly not crying at night and losing any sleep over it but there are obviously certain restrictions on getting players into here," Rodgers told Sky Sports News.
"In terms of Eidur, he won't be coming. I spoke to him again last night and I think he will probably end up choosing to go to London."
Rodgers added: "It is a wonderful city here and a wonderful club but like all newly-promoted clubs, when you come up it can be difficult to get players.
"But I'm very fortunate to have a really good group of quality players here and I feel I only need to add three of four to that to give us a fantastic opportunity to stay in this league.
"This club and the players have earned the right to be here - no matter what people will say we deserved the right to be here."