Sunderland are yet to make a signing during the summer transfer window.
The Black Cats have been frustrated in the transfer window so far, and they are yet to make a signing.
However, Allardyce insists that his backroom staff are determined to recruit some new players soon.
And he said: “We want to improve the squad with two, three, four players as quickly as we can. It’s been a huge demand on all our resources to get those players.
“We’re trying to work in the market shrewdly and to do get the best value for money we possibly can.
“Hopefully the fans will be a little bit patient, but I have to admit myself that my patience is wearing thin - very, very thin indeed.”
Sunderland were expected to invest heavily in their squad this summer, but their plans have been disrupted so far.
The Black Cats have been largely frustrated, with Allardyce determined not to pay over the odds for players.
Sunderland did come close to signing Davide Santon from Inter Milan, but the deal fell through at the last minute.
The Wearsiders are currently in Austria on pre-season training, as they prepare for the new campaign.
Sunderland’s competitive season gets underway next month, with a match against Manchester City.