Redknapp added two more players - Leroy Fer and Eduardo Vargas - to his squad in the last couple of days as he was preparing for the trip to former side Tottenham on Sunday.
The 67-year-old is not ruling out another move before the transfer window shuts on September 1, with Wilfried Zaha having been linked with a loan deal from Manchester United, but he is not too concerned if his dealings for the summer are already finished.
"The club have been great, I have been pleased with the players we have brought in, it has made a big difference," Redknapp said.
"We came back in pre-season and we were really, really short of numbers and we have brought some quality players in. It is up to us now to get on and do the job, if there is another one to come in then great - if not then we will see."
Redknapp will have no qualms about making another addition to his squad, but he admits any more deals will most likely have to be temporary, as the purse-strings are a little tighter for him now.
"We were the loan Rangers in the Championship last season," Redknapp joked.
"We've still got two loans that we can use from the Premier League if we want to. If they were to loan him (Zaha), if he did become available I'm sure he would be a player a lot of clubs would be interested in. If we thought he was available he would certainly be of interest."
And Redknapp is confident he will not have to find a late replacement for Loic Remy, who had been linked with a move away over the summer but started their Premier League opener against Hull City last weekend, a game they lost 1-0 after Charlie Austin missed a penalty.
"I'm confident he'll be here," he said.
"I've spoken with Loic, he's been excellent in training and his attitude has been world class. Unless a top six club comes in, I think he'll be happy to stay here. He's seen we've brought some good players in.
"There's been no Tottenham enquiry - there's been talk of the chairman talking to Daniel (Levy), but certainly I've not been involved."