Tsipras: 'No' vote not a mandate to clash with Europe

Stelios Kouloglou, an MEP with Greece's ruling Syriza party, told CNBC that nobody had predicted this result. "Even with the banks closed, people can't get money anywhere - and still, more than 60 percent voted to support the government. This is a huge vote," he said on Sunday.

Following news of the "no" victory, opposition leader Antonis Samaras stepped down.

Kouloglou said the deal proposed by creditors—and voted on by Greeks in this referendum—was "not practical."

With the result, Tsipras "has more strength to negotiate. The real (aim) for us is not to leave the euro zone, but to negotiate a better deal," he added.

Before polls closed, Greek Finance Minister Yanis Varoufakis told CNBC that the government could potentially reach a deal with lenders within 24 hours if the "no" campaign was successful.

'I think this is the end'

Despite this optimism regarding an imminent deal, however, five months of talks have so far failed to reach an agreement. Read MoreGreek banks may not re-open any time soon The radical leftwing Greek government and the so-called Troika which oversees its bailout – the International Monetary Fund, European Commission and European Central Bank – disagree on the reforms and the accompanying austerity measures required before Greece receives further financial aid.

The next steps for Greece are unclear, however, as the reform proposals being voted on are no longer on the table, after the country's bailout program effectively ended at the end of June.

"I think this is the end — Greece will ultimately have to leave the euro," said Philippa Malmgren, founder of advisory group DRPM. She said one option would be for Greece to temporarily leave the single currency region with the aim of re-joining once it had brought down its debt-to–gross domestic product (GDP) ratio.

Read More: Live blog: Greece votes 'no'

"It's true the banks won't have enough cash to meet the demands of the depositors – they're actually broke… Now the possibility is Greece actually abandons the positions it has had and it goes back to market forces. I'm optimistic about what it will bring," Malmgren told CNBC.

Practicalities?

If Greece does leave the euro zone, it will be the first country to do so since the currency's inception in 1999. It will also set a worrisome precedent, as the Maastrict Treaty was originally conceived to be irrevocable. A "Grexit" could also open the door for other debt-strapped euro countries to walk through.

Francesco Papadia, former Director General for Market Operations at the European Central Bank, said that Greece's central bank could potentially be removed from the European Central Bank system "in weeks not months."

"If that needs to be the case, that can be done quickly," he told CNBC on Sunday.

"It will be complicated. I'm not sure there is a plan to do it, but my former colleagues will know how to do it if needed."

The vote comes after Greece effectively defaulted this week on 1.6-billion-euro ($1.7 billion) payment due to the IMF, and its domestic financial system is under severe pressure, with capital controls imposed in order to prevent bank runs. However, British Conservative MEP Daniel Hannan says the long-term future for Greece now looked much better and there is "light at the end of the tunnel." "A default and a devaluation is the least bad option for Greece," he told CNBC on Sunday.

"It's going to be tough in the short-run. But if Greece gets this thing right, if it goes to exploit its competitive advantages could bounce back hugely impressively."