In a wide-ranging speech at the German Council on Foreign Relations think tank in Berlin, Ms Lagarde also called for an additional $500bn (£320m) for the IMF as it seeks to keep afloat countries battered by the crisis.
And she had a dire warning for policymakers if they failed to do what was necessary, saying the world could slide into a "1930s moment" of isolationism, which led to the Great Depression and eventually to world war.
On the eurozone, Ms Lagarde acknowledged that a great deal had already been accomplished but that the policies agreed so far "form pieces, but pieces only, of a comprehensive solution."
She said the crisis-wracked eurozone had to focus on rediscovering growth as well as bolstering its defences against contagion from the debt turmoil and pulling closer together politically and economically.
To spur growth, she called indirectly on the European Central Bank to lower interest rates, already at a record low. With inflation falling sharply, "additional and timely monetary easing will be important," she said.(means Inflation)
"We need a larger firewall," she added. "Without it, countries like Italy and Spain that are fundamentally able to repay their debts could be forced into a solvency crisis by abnormal financing costs."
She proposed "folding" the leftover cash in the eurozone's current rescue pot, the EFSF, into the permanent ESM bailout fund when the latter comes into force, likely in the middle of this year.
However, departing from the text of her speech, she stressed: "I am not talking about doubling" the €500bn ESM as reportedly wanted by Italian Prime Minister Mario Draghi.
In addition, she said the ECB should "provide the necessary liquidity support to stabilise bank funding and sovereign debt markets".
And she argued that "political agreement on a joint bond to underpin risk sharing would help convince markets of the future viability of European economic and monetary union."
The creation of such a "eurobond" has long been a contentious issue among top policymakers, with the European Commission and France being in favour of such an instrument but German Chancellor Angela Merkel is strictly opposed for now.
Partly to assist in battling the crisis, both in the eurozone and further afield, Lagarde said: "I am convinced that we must step up the fund's lending capacity."
"In the coming years, we estimate a global potential financing need of $1 trillion. To play its part, the IMF would aim to raise up to $500 billion in additional lending resources," she said.
And following what she termed "so much loose talk about special 'European bailouts'," she stressed IMF help was "for all members" but insisted that "any support we provide to euro area countries must be anchored in a clear policy framework for the entire euro area."
After a turbulent 2011, Ms Lagarde announced that Tuesday's updated IMF economic projections would result in "lower growth forecasts for most parts of the world."
"Even these lower forecasts assume a constructive policy path that is by no means assured," she cautioned.
And she warned that if policymakers failed to grasp the seriousness of the situation, "we could easily slide into a '1930s moment'."
"A moment where trust and cooperation break down and countries turn inward. A moment, ultimately, leading to a downward spiral that could engulf the entire world."
However, Ms Lagarde said, "I believe we can avoid such a scenario ... although the economic outlook remains deeply worrisome, there is a way out."