Draghi also told the Financial Times in an interview that the ECB could not start printing money, adding that any country leaving the euro would be worse off and would still have to go through the same reforms.
He said there was no long-term trade-off between growth and austerity.
To have a return of confidence in the eurozone, suffering from a sovereign debt crisis which has engulfed several countries, there is a need "to have a firewall in place which is fully equipped and operational. And that was meant to be provided by the EFSF," Draghi said, referring to the European Financial Stability Facility.
"If one can show its usefulness in its present size, the argument for its enlargement would be much stronger," he said.
Draghi, who in November became the third ECB president in its 12-year history, said the longer it took to put together a firewall to stop market contagion, the more expensive it got.
"The delay in making the EFSF operational has increased the resources necessary to stabilising markets," he said.
"A process that is fast, credible and robust needs less resources," Draghi said, adding that the ECB aims to provide the eurozone rescue fund assistance from January.
The ECB has been tasked with aiding the EFSF in its market interventions once it is ready to start spending its funds.
Draghi declined to give a clear answer when asked whether the ECB would keep buying government bonds through its securities markets programme, or SMP, once the EFSF entered the picture.
"We have not discussed a precise scenario for the SMP. As I often said, the SMP is neither eternal nor infinite," he said. So far, the ECB has spent more than €200 billion to buy sovereign bonds of countries mired in the debt crisis.
Draghi also said it was not the role of the ECB to instal targets for government bond spreads, adding that those depended on rules governments put in place.
"Sovereign spreads have mostly to do with the sovereigns and with the nature of the compact between them. It is in this area that progress is ongoing. Monetary policy cannot do everything."
No money printing press
Draghi warned against putting expectations for the ECB to solve the debt crisis by becoming a lender of last resort to governments.
Asked if the ECB could engage in full-blown quantitative easing – printing money – to buy government bonds and ease their funding strains, he said that would be counterproductive.
"The important thing is to restore the trust of the people - citizens as well as investors - in our continent. We won't achieve that by destroying the credibility of the ECB".
Draghi tried to offer solace to indebted countries by saying that consolidation would not hurt growth in the long run. He said countries can reduce the short-term impact by reforming their economies, adding that consolidation can make funding cheaper as markets grow more confident.
But he said an effort must be made across the board and that improving governance in the common currency area is an important part of that package.
"Austerity by one single country and nothing else is not enough to regain confidence of the markets."
Neither was leaving the eurozone an answer to the problems, Draghi said, dismissing talk of Greece being better off were it to leave the euro.
"This wouldn't help. Leaving the euro area, devaluing your currency, you create a big inflation, and at the end of that road, the country would have to undertake the same reforms that were due to begin with, but in a much weaker position."
Draghi also told the newspaper that tight funding conditions in the interbank market were becoming a growth risk.
"These challenging funding conditions are now producing a credit tightening and have certainly increased the downside risks for the euro area economy," he said.
He pinned hopes on the ECB's recently announced 3-year liquidity operation to help improve banks' situation, and added it was up to the banks how they would spend the funds they are going to bid for – with buying government bonds one option.
"Coming back to what banks are going to do with this money: we don't know exactly. The important thing was to relax the funding pressures. Banks will decide in total independence what they want to do," the ECB head told the newspaper.
"One of the things that they may do is to buy sovereign bonds. But it is just one."