City regulator boss Andrew Bailey has told the Treasury Committee there were "frank conversations" with TSB about the way it communicated information about its IT meltdown.
Mr Bailey, chief executive of the Financial Conduct Authority (FCA), said: "I think there is an onus in my view on over-communicating in these situations."
He later added: "A more straightforward recognition of what the situation was would have been helpful."
Up to 1.9 million people using TSB's digital and mobile banking found themselves locked out of their bank accounts following the migration of data on customers from former owner Lloyds' IT system to a new one managed by current owner Sabadell.
Mr Bailey said the watchdog will be looking at current account switching levels in the wake of the problems, including whether switching is happening effectively or not.
The committee heard some TSB customers have already started receiving compensation.
Asked about how quickly a compensation system should be set up, Mr Bailey told the committee: "It should happen quickly. It's not complex and it's clear what happened. The timeline is quite short in terms of what went wrong."