This is a reasonable question – the answer to which is that the fact of a central bank being independent does not mean that it is unaccountable. Indeed, independent central banks, such as those in the ESCB, are accountable to the public in that they have to fulfil their mandate to maintain price stability.
If the Eurosystem were to fail to fulfil its mandate, it would have to explain to the public at large why this had happened. There are various appropriate ways of communicating our policy.