Even as Cyprus's President Nicos Anastasiades addressed the nation on Sunday night, saying savers would be compensated by shares in banks guaranteed by future natural gas revenues, critics still cast a wary eye on the bailout deal.

Over the weekend, analysts warned the decision by the euro zone to force bank depositors in Cyprus to contribute towards a bailout—a first in the euro zone debt crisis—could hurt other peripheral nations, the euro and the global stock market rally.

In his televised address, Anastasiades said he had to accept a tax on bank deposits in return for international aid, or else the island would have faced bankruptcy.

"The solution we concluded upon is not what we wanted, but is the least painful under the circumstances," Anastasiades said.

Doug Kass of Seabreeze Partners on Twitter predicted European stock markets could fall 3 to 4 percent on Monday, while the S&P 500 could fall 1.5 to 2 percent and Spanish and Italian 10-year yields could jump 15 basis points.

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