Some observers had predicted that efforts to renegotiate the bailout could lead to a run on Greek banks and deeper misery.
"Don't underestimate the capacity of the Greek people to rise to the occasion," Petros Doukas, a former New Democracy lawmaker and deputy finance minister, told CNN.
"What's very clear is the Greeks today voted, including those that voted for Syriza, in favor of the euro and the European Union," Doukas said. He predicted that Greece could negotiate better terms with its creditors, who understand "that you can only squeeze so much so fast out of a country and out of its people."
Greeks have been suffering under painful austerity measures, high unemployment and a long-running recession.
The country must identify additional budget cuts by the end of June to be considered compliant with the terms of its bailout.
German Chancellor Angela Merkel, Europe's powerful advocate for balancing budgets to build a strong basis for economic growth, had urged Greeks not to walk away from the international loan deals.
"We will stick to the agreements. That is the basis on which Europe will prosper," she said Saturday.