The Unite union said its poll of more than 1000 adults found almost three out of four had suffered because bank machines were out of order.
The findings follow huge problems on Sunday when Lloyds Banking Group customers were left unable to use their cards or withdraw cash for hours following an IT glitch.
Debit card transactions were disrupted for three hours and cash machines for four and a half hours before the difficulties were resolved, hitting customers of Lloyds, TSB, Halifax and Bank Of Scotland.
The Lloyds group apologised to its customers after it was revealed about half of its 7000 ATMs were affected.
Unite said its poll showed almost two thirds of those questioned wanted to see more staff in bank branches, while one in five was unsure about how to use a machine.
One in 10 said they had been hit by fraud because of hacking or tampering with machines.
Dominic Hook, Unite national officer, said: "The speed that UK banks are moving towards increased automation across their branches is incredibly significant for all bank customers.
"The poll shows the significant reputational damage the banks will suffer if they ignore the needs of their customers.
"There is no doubt about the importance of frontline bank staff.
"This evidence that customers want well-staffed branches and would prefer to deal with the highly trained and professional staff that currently service their branches should set off alarm bells for the industry.
"Their customers don't want to see empty, soulless branches."
TSB chief executive Paul Pester apologised to customers who had been affected by the problems on Sunday and said it was due to a "server failing".
He said: "The cause of the problems at TSB is now fixed. It will take a while to sort the backlog. Sorry once again to all our customers affected."