Fears of contagion from the region's sovereign debt crisis also put otherwise healthy banks under suspicion and there are still concerns over the number of non-performing loans (NPLs) on bank balance sheets, especially in Italy, where banking stocks have taken a beating this year.
Italy is mulling the creation of a so-called "bad bank" and has attempted to quell worries over its financial system by pressing on with structural reforms.
Italian Economy Minister Pier Carlo Padoan came to the defense of the ECB's QE program, commenting that the efficacy of monetary policy depended on the accompaniment of structural policies carried out by governments.
He mentioned Italy's labor market reforms which were starting to "bear fruit" in Italy and said that his country would announce more reforms in the coming week and would strengthen the Italian banking system.
"My point is that on the impact of monetary policy, there is a division of labor here. National governments, and certainly my government, know very well that to make the most of what I consider a positive policy stance (by the ECB) we need to do our homework (on reforms) and we're doing it," he said.
Italian banking stocks have seen tumultuous start to the year as fears grow over the stability of the financial sector and the weight of bad loans. Padoan said a bad bank should have been set up a long time ago, and said the current government was working hard to resolve the issue with the European Commission, saying "we have been working on a continuous basis for months."
Francisco González, chairman and chief executive of Spanish banking giant BBVA, knows something of "bad banks"; Spain set one up following a collapse in its banking sector in 2012/2013 to absorb the sector's NPLs.
"Spain has bitten the bullet for about three or four years by putting the house in order and we have taken very good decisions in mainly scrapping the failing banks and now the system is working much better," González told the panel.
He warned that the danger was still present, however, saying that Europe's banks were in for a "tough ride."
"The banking system has to take this situation very seriously, apart from this present situation (of low interest rates and low inflation), there's a big threat for the banking system from the digital disruption."
He said Europe was lagging behind in terms of financial innovation.
Another challenge for Europe was the implementation of a banking union in the euro zone and new regulation.
Chastened by the financial crisis, which saw Greece come perilously close to bankruptcy and an exit from the euro zone, Europe has looked to prevent such a crisis from happening again.
In order to prevent future financial shocks permeating the entire region, the euro zone is creating a more integrated and regulated banking union in order to create what the European Commission hopes will be a "safer and sounder financial sector for the single market."
Initiatives within the union include creating a single supervisory mechanism overseen by the European Central Bank, a single resolution mechanism – and crucially, a single resolution fund to rescue banks – for the banking sector.
Lord Jonathan Hill, commissioner for Financial Stability, Financial Services and Capital Markets Union in the European Commission, told the panel that the banking sector was now much stronger thanks to new regulations.
"We should keep reminding ourselves that the European banking sector is a lot stronger, a lot more resilient and better governed than it was during, before and immediately after the financial crisis.
With 40 separate pieces of new bank and financial services legislation introduced over the last five years, there has been criticism from banks who say it has hindered their operations.
Hill objected to that criticism, saying the sector was more transparent now and safer for consumers.
Follow CNBC International on Twitter and Facebook.