Sunderland were on the verge of making their first signing of the summer last week after former Newcastle defender Santon flew to the North East to finalise a £3million move from Inter Milan.
A new right-back had been one of Allardyce's top two priorities in the transfer market, yet the move collapsed due to last-minute issues in the negotiations between Sunderland and Inter.
And Allardyce is struggling to contain his frustration that Sunderland still haven't made a transfer breakthrough, with the Black Cats beginning their pre-season friendly programme at Hartlepool next week.
He said: "There's no doubt that the one big thing I have to cover is striving hard every single day on the phone with all our recruitment people to find the right deal for the right player.
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"It was a huge disappointment for me that I was not able to clinch the Davide Santon deal, just a couple of days ago.
"We want to improve the squad with two, three or four players as quickly as we possibly can.
"It's been a huge demand trying to find those players, but we'll continue that until we're successful.
"Hopefully fans will be a little bit patient.
"I have to admit myself that my patience is wearing thin, but we have to keep trying to bring in those three or four players as quickly as possible."
Sunderland's coffers have been boosted by an extra £30million with the new television deal, yet Allardyce believes that has actually made the transfer market more complicated due to rising price tags
"Everybody think's the money will make things easier, but it's actually made it more difficult because we all have the same money," he added to the club website.
"Everything has got more expensive. A player who cost £10m last year, will now cost £20m.
"That is the unfortunate market we're working in.
"We're trying to work as shrewdly as possible to get the best value we can."