Redknapp has added goalkeeper David Stockdale, defender Marc Roberts and midfielder Cheikh N'Doye this summer.
Ravel Morrison and Simeon Slavchev also remain on trial with the club, but the Blues manager wants more additions before the season begins on Saturday.
"We're a little bit short at the moment - we need to improve the squad this week if we can," he told BBC WM.
"We've been trying, but it's been very difficult to get the players in who we've been chasing. Hopefully we'll get there - it's not been through lack of effort."
Redknapp confirmed an interest in Bristol City's Aden Flint, who may be available following the arrival of Nathan Baker from Aston Villa.
"I like him but we'll only pay what we can - if he's too expensive then we'll move on," he said.
Following the 2-0 friendly loss to Swansea on Saturday, Redknapp also said defender Ryan Shotton could leave if the club's valuation is met.
If Shotton were to go that would leave Birmingham, who missed out on John Terry to rivals Villa, with just two centre-backs going into the opening game of the Championship season at Ipswich on Saturday.
"I'm not frustrated. I'm just desperate to do well, but I need the tools to be able to do that," Redknapp said.
"If I get the tools I'll do that, if I don't then it's going to be difficult."

Conrad Clitheroe and Gary Cooper, both from Stockport, and expat Neil Munro were reportedly taking notes near Fujairah Airport, 80 miles from Dubai, when they were arrested in February.
Relatives were told they were held for "national security" reasons. The men insisted they did not take photographs.
The Abu Dhabi hearing is due on Monday.
Mr Clitheroe, 54, and Mr Cooper 45, were visiting their friend Mr Munro, who was born in Manchester, when they were arrested on 22 February by an off-duty police officer who had seen them monitoring planes from a car.
They were near Fujairah Airport, where older and rarer aircraft can be seen.
A local police official said the men had been taking photographs near an airport and were using a telescope.
The men are expected to argue their actions were misinterpreted and are understood to be hoping to be granted bail.

The 25-year-old moved to the Red Rose from Somerset in 2013 and his new deal ties him to the club until 2019.
Short-format specialist Buttler has scored England's three fastest ODI centuries, including a 46-ball ton against Pakistan last year.
"Jos is one of the most talented cricketers in the game," said cricket director and head coach Ashley Giles.
"His presence in last year's T20 Blast final at Edgbaston was a factor in us winning the competition.
"Jos is a great guy to have in the dressing room too and his experience at international level really benefits the squad."
Buttler, who has been playing in the Indian Premier League with Mumbai Indians, will return to Lancashire for Friday's T20 Blast home game against Durham.
Birmingham City will face a "difficult" season if they cannot sign new players this week, says manager Harry Redknapp.
[NEXT_CONCEPT]
A court hearing for British plane spotters held over allegations of suspicious behaviour in the United Arab Emirates has been postponed for a week.
[NEXT_CONCEPT]
England wicketkeeper Jos Buttler has signed a new three-year contract with Lancashire.