Speaking in Brussels, he also called for the "structural reforms" he says are necessary to "restore clarity and confidence" among Eurozone members.
He told a conference on Thursday, "Many reforms have been implemented in recent years, especially in those countries worst hit by the crisis.
"The benefits can now be seen but there are many more benefits still to aim for, and so much more needs to be done."
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Addressing the Brussels Economic Forum, Draghi, a former governor of the Bank of Italy, said EU leaders should press ahead with reforms that would create more jobs, in order to help save the Eurozone from its ageing crisis.
Then Italian said there was a "critical need" to restore clarity in the Eurozone, adding, "We all know the current institutional set up is incomplete. There is a large degree of agreement on what its shortcomings are and proposals have been put forward on how to overcome them.
"Progress in this field is necessary for the long term but also for the short term. The best way to raise output today is to remove the drag on confidence that results from such uncertainties."
The forum heard that Europe is at risk of suffering lasting economic damage from weak productivity and low growth.
Draghi, ECB boss since 2011, argued that monetary policy alone cannot end the EU's economic malaise.
"We cannot avoid the fact that, over time, the inherent speed limits resulting from the euro area's unfavourable demographics will start to bite," Draghi said in his speech at the forum, the 16th year it has been held.
The cost of a delay in implementing the necessary reforms was, he said, "simply too high."
The Eurozone economy grew by 0.6 per cent between the final quarter of 2015 and the first quarter of this year, but it took almost eight years to return to pre-crisis growth levels and continues to operate below full capacity.
A return to maximum capacity would, Draghi said, have been quicker "if fiscal policy had been more supportive."
Draghi, who delivered a keynote lecture, said, "We do not let inflation undershoot our objective for longer than is avoidable given the nature of the shocks we face.
"For others, it means devoting every effort to ensuring that output is returned to potential before subpar growth causes lasting damage.
"There are many understandable political reasons to delay structural reform, but there are few good economic ones. The cost of delay is simply too high," he added.
Singling out areas for improvement, Draghi said the Eurozone was lagging behind in innovative capacity, particularly in the services sector, and needed to utilise the latent potential in the euro area labour force, which can be "unleashed with appropriate labour market and activation policies."
Another keynote speaker at the forum, the EU's flagship annual economic event, was Valdis Dombrovskis, European the Euro and social dialogue Commissioner.
Outlining efforts to get the Eurozone "back on track," Dombrovskis said, "Our part of the job is clear: as the European economy is slowly but surely gaining force, we need to strengthen the recovery. For this, we have three immediate priorities: re-launching investment, continued structural reforms, and responsible fiscal policies.
"But today's discussions will focus not only on the immediate macroeconomic challenges but also on the road ahead: how do we make the Economic and Monetary Union more resilient to future shocks; and how do we re-launch the process of convergence within the euro area and the EU as a whole."
He added, "The EU is already much more resilient than it was just a few years ago.
"And we have already seen it during the most recent Greek crisis. It remained just that: a Greek crisis - serious enough in itself - but there were very little spill over effects to other euro area countries and the stability of the euro area as a whole was not in question."
The one-day forum was attended by more than 1000 EU policymakers, financial experts, business leaders and civil society representatives.
Also addressing the conference, European economic and financial affairs Commissioner Pierre Moscovici said, "Europe is emerging from an economic crisis of unprecedented proportions, one which laid bare the need for deep reforms and a comprehensive policy approach."
The official said that to effectively tackle the risk of persistent low growth, near-zero inflation and high unemployment, "we need to combine structural, fiscal, and monetary policies, in an integrated and growth-friendly approach."
He added, "This means, in my view, tackling both the demand and supply sides of our economies, because the impact of the crisis has been both cyclical and structural."