A computer problem at Kirkintilloch's new post office, recently relocated to WH Smith in the town's Cowgate, meant that staff were unable to payout pensions or benefits in the run-up to Christmas.
Staff were unable to access the online banking system between lunchtime on Saturday, December 22, and Christmas Eve.
Customers were told they would need to travel to another post office branch or return after the Christmas break.
One pensioner told the Herald: "It was unbelievable. I went in for my pension and there was a big queue of people trying to get their money.
"Some customers were getting very angry as they wanted their money in time for Christmas."
Margaret Smith, from Kirkintilloch, took an elderly friend to the post office on Christmas Eve to pick up her pension. She was shocked to be told that they would need to travel to Bishopbriggs to get her money.
Margaret said: "I felt that it was an outrageous situation. My friend is 85 and couldn't get over to Bishopbriggs. It's okay for people who have money in the bank, but for some of us this is the only cash we get, and we rely on it.
"There were lots of people there who were planning to go Christmas shopping, but they weren't able to. It's disgraceful."
David Whitton, MSP for Strathkelvin and Bearsden, said: "This hasn't been raised with me by any of my constituents, but I hope that WH Smiths will carry out an investigation into what went wrong and ensure that it does not happen again."
A spokesperson for Post Office Ltd said: "We would like to apologise for any inconvenience caused to customers because of technical problems at the Kirkintilloch post office branch from lunchtime on Saturday, December 22 to Monday, December 24.
"Due to circumstances outwith our control the computer system was unable to process any on-line banking transactions.
"In conjunction with our service providers an engineer visited the office, the fault was identified and was rectified at 3.30pm on Christmas Eve.
"We regret the obvious inconvenience caused to customers and apologise to anyone who had to travel to alternative branches to collect pension or benefit payments."