Around 20 Tesco's staff were still in the building.
As the Securicor drivers opened the machines, a red Vauxhall Cavalier reversed through the shop's circular entry doors, smashing the glass.
Two raiders - believed to be male - jumped out of the car, wearing balaclavas and carrying at least one handgun.
"The staff, both Tesco's and Securicor, reacted very quickly," said DI Smith.
"As soon as they heard the noise, they moved well away from the doors. They retreated back through the store, which was the most sensible thing to do. With a weapon involved, there was no other choice."
The raiders left a few minutes later, with four cash boxes containing £32,400. The car was found by police in the car park of the Red Lion pub in Pickmere on Sunday afternoon.
Police are appealing for witnesses to the robbery, and also for anyone who saw the car, a red J-registration Vauxhall Cavalier hatchback, leaving Northwich or arriving in Pickmere on Wednesday night.
The gun, a Colt revolver, was found inside the store. It contained a full round of six bullets.
"Certainly two individuals were involved, but there may have been more, and possibly a second car," said DI Smith.
"They were wearing dark clothing, but beyond that we have little information on them. That is why we urgently require help from the public to catch these people."
If you have any information about the robbery, ring Northwich police on 01606 48000.
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