That concern was evident in markets. The euro currency, used by more than 330 million Europeans, initially rose against the dollar to about $1.30 on news of the bailout agreement, but tanked below $1.29 — its lowest level since November — following Dijsselbloem's remarks. European stock market indexes also lost their earlier gains, with bank shares hardest-hit, particularly in financially weak countries like Italy and Spain.
On Wall Street, stocks reversed an early rise as traders returned to worrying about the eurozone, and the Dow Jones industrial average closed down 0.4 percent.
After a whirlwind of nervous market reactions, Dijsselbloem issued a terse clarifying statement, saying Cyprus was "a specific case with exceptional challenges which required the bail-in measures."
"Macro-economic adjustment programs are tailor-made to the situation of the country concerned and no models or templates are used," he added.
Under the new Cyprus bailout plan, the bulk of the funds will be raised by forcing losses on accounts of more than 100,000 euros in the country's second- largest lender, Laiki, and its top lender, Bank of Cyprus, with the remainder coming from tax increases and privatizations.
People and businesses with more than 100,000 euros in their accounts at Laiki face significant losses. The bank will be dissolved immediately into a so-called bad bank containing its uninsured deposits and toxic assets, with the guaranteed deposits being transferred to the Bank of Cyprus.
Deposits at Bank of Cyprus above 100,000 euros will be frozen until it becomes clear whether or to what extent they will also be forced to take losses. Those funds will eventually be converted into bank shares.
It's not yet clear how severe the losses will be to Laiki's large bank deposit holders, but the euro finance ministers noted that the restructuring is expected to yield 4.2 billion euros ($5.4 billion) overall. Analysts have estimated investors might lose up to 40 percent of their money.
Speaking about the marathon 10-hour negotiations in Brussels that resulted in the deal, Cyprus President Nicos Anastasiades said "the hours were difficult, at some moments dramatic. Cyprus found itself a breath away from economic collapse."
The agreement, he said, "is painful, but under the circumstances the best we could have ensured. The danger of Cyprus' bankruptcy is definitively overcome and the tragic consequences for the economy and society are averted."
Juergen Baetz in Brussels contributed to this story.