German Chancellor Angela Merkel's cabinet approved the 2010 budget this month, which foresees a record €85.8 billion in new debt next year.
"In Europe and around the world, there are lessons to be learned from the financial crisis to make the financial system more resilient." He urged banks to help ease a credit crunch by making loans available.
"In the eurozone, budget deficits should be reduced in 2011 at the latest, in some countries already in 2010, to preserve faith in state finances," Trichet told the newspaper.
"Banks must live up to their central role in providing credit to the economy," Trichet said.
Greece, which is also a member of the eurozone, saw its sovereign credit rating downgraded this month due to a ballooning public deficit and debt.
Its debt is now estimated at €300 billion ($430 million), three times the size of Germany's, which is the biggest eurozone economy. The crisis has roiled markets and pushed down the value of the euro.
Athens' public deficit is likely to rise to 12.7 percent of output this year, far exceeding the limit of 3.0 percent for countries that use the single European currency.