Barroso hinted that the European Commission might be prepared to relax some of the targets set for countries in trouble to restructure their economies.
Barroso, a former prime minister of Portugal, told a seminar for Portuguese diplomats that 2012 had ended on a "positive note" for the European Union.
"I think it is fair to say that the perception of risk in the eurozone has disappeared," he said.
"Investors have understood that when European leaders commit themselves to doing everything to safeguard the integrity of the euro, they mean business," he said.
But the situation in Europe remained "difficult", notably because unemployment was expected to be high in 2013.
Programmes to correct the economies of several EU countries were having a recessionary effect even though the measures created the conditions for firm medium and long-term growth, Barroso said.
He stressed that efforts to balance public finances and to reform economies had to continue.
But he also said that "the European Union is ready to analyse the trajectories of different programmes," in a reference to conditions attached to rescue packages for several countries being helped by the EU and in several cases also by the International Monetary Fund.
The eurozone countries being helped most directly are Greece, Ireland and Portugal.
Barroso said that the EU could "make adjustments and the calibration needed so as to minimise the social effects" of the reforms.
He referred specifically to the case of Portugal which has been receiving rescue help since May 2011.
He said that the country was experiencing "a true situation of social emergency".
Official forecasts suggest that the unemployment rate will rise to 16.4 percent by the end of 2013.
Portugal is having difficulty meeting its targets under the bailout programme.
Barroso recalled that the three bodies behind the rescue programme, the IMF, the EU and the European Central Bank had decided to relax the target for reducing the public deficit, setting a figure for the deficit of 5.0 percent of output this year instead of 4.5 percent and of 4.5 percent for 2014 instead of 3.0 percent.