Jose Manuel Barroso, who left the key post last October, said that Alexis Tsipras's Syriza-led administration lacked experience.
Greece's demands were "completely unacceptable to other countries", he told the BBC's Business Live programme.
In its election campaign, Syriza promised to ease economic austerity.
Mr Tsipras pledged new jobs and a rise in the minimum wage. But Greece's creditors have made it clear they will not support a bailout for the country unless there is a comprehensive plan to reduce spending and increase revenues.
On Wednesday, the Greek government submitted fresh reform proposals.
The new plan foresees increasing government revenues through a crackdown on tax evasion and fraud, and a new lottery designed to encourage payment of sales tax.
But it also includes extra spending, including increased pension payments and and rise in the minimum wage.
Greece's creditors will now decide whether these latest reform proposals go far enough to unlock the bailout money.
In the interview, Mr Barroso pointed out that there were poorer countries lending money to Greece who would not support the idea of Greece's debts being written off.
He called on Greece to take responsibility for its financial plight and implement structural reforms, which was now the most important issue for the country.
"It was not Germany or any other member of the EU that created the problems in Greece - the problems in Greece are structural: low productivity and previous governments."
Nations such as Ireland, Portugal and Spain had come back from the financial brink and Mr Barroso said Greece could do the same: "There is nothing regarding Greece that prevents it being successful, but... bad politics have created a lot of problems for Greece."
Greece's previous proposals failed to satisfy its main creditors, the European Commission, the European Central Bank and the International Monetary Fund (IMF).
But France's finance minister, Michel Sapin, said Greece's new proposals did represent some improvement in Athen's position.
"There is progress with the last list... Is there a need for more progress? Yes - in the quantification of the measures," he said.
A decision may not come before Greece is due to make a â‚¬450m (Â£330m) payment to the IMF on 9 April.
Eurozone finance ministers are likely to reserve any formal judgement for the next scheduled meeting in Riga on 24 April.
Despite the ongoing bail-out negotiations, Mr Barroso said a Greek departure from the eurozone was still a possibility. He said that would still be "negative", but that he believed it would be less damaging now because financial markets were much more confident than they had been in recent years.
However, he added that a "Grexit" would still leave the idea of monetary union in doubt. "It breaks a taboo and sets a precedent," he said.
The former EC chief and Portuguese prime minister also reiterated his view that Britons would be worse off if the UK left the European Union.
"I believe they would lose a lot if [the country] leaves the EU, because today, in the 21st century, versus the US, China, countries of 60 million people cannot speak at the same level - they do not have the same leverage - and we have to use the EU and our common leverage to count in the world."
Mr Barroso, 59, is now a visiting professor at Princeton University and the University of Geneva.
Business Live airs at 07.30GMT each weekday on BBC World TV.
The Greek government made "completely unrealistic promises" to voters that it cannot now fulfil, the former European Commission president has said.