The problem affected customers with Halifax, Lloyds, Bank of Scotland and TSB from yesterday afternoon.
Carl Bullivant tweeted: "Wife's card declined in Asda had to go get my card from home how embarrassing standing and waiting £poorbankingservice."
Essie Young wrote: "Didn't even want to be a @TSB customer when LTSB split! Couldn't buy my twins bday presents today with TSB card! £fuming £customerservice."
Another customer tweeted: "@TSB left me unable to pay for my shopping and no access to my money. TSB are a joke."
Another Twitter user wrote: "This problem is also affecting Halifax debit cards as I found out trying to pay for lunch with my wife!"
When the problems arose, TSB chief Paul Pester tweeted: "My apologies to TSB custom-ers having problems with their cards. I'm working hard with my team now to try to fix the problems." He also took to Twitter to respond directly to unhappy customers.
He said a quarter of its customers' debit card transactions had been affected after problems with two out of seven IT servers and that the problem was resolved by 7.30pm.
In a statement, Lloyds Bank-ing Group said: "Although the majority of transactions were unaffected, we are very sorry for the inconvenience that this will have caused.
"At the same time, some customers encountered problems at approximately half of our 7000 ATMs. This was resolved by 7.30pm, and all of our ATMs are now working."
TSB has about five million UK customers and is in the process of being split from Lloyds Banking Group, the UK's largest retail bank.
In 2012, a major IT failure locked many RBS, NatWest and Ulster Bank customers out of their accounts for several days. The issue was particularly bad for Ulster Bank, with customers facing access problems for weeks.