The comments on Wednesday by Valdis Dombrovskis, the Commissioner for the euro and social dialogue, come on the day the Commission publishes its annual analysis of the economic and social situation in member states.
The report says member states are making headway in implementing the individual policy guidance they received last year on boosting investment, pursuing structural reforms and ensuring responsible fiscal policies.
The 27 country reports exclude Greece, which is under a stability support programme.
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The Commission concludes that in most countries, economic recovery has contributed to declining unemployment rates, although these are still above pre-crisis levels.
Large current account deficits have been corrected, and sizeable stocks of private, public and external debt have started falling as a share of GDP.
However, a number of risks remain; high current account surpluses are only being adjusted to a limited extent.
Speaking in Brussels at a news conference where the reports were published, Dombrovskis said, "Today's analysis shows that our policy strategy based on boosting investment, pursuing structural reforms and sound budgetary policies is bearing fruit.
"This is why, rather than giving people false promises that cannot be delivered, we should stay the course and continue to address the legacies of the crisis and structural weaknesses in our economies.
"EU and national policies should aim to make our economies more resilient and ensure that the recovery is felt by all."
His comments were echoed by Commissioner Marianne Thyssen, in charge of employment, social affairs, skills and labour mobility.
She said, "Europe is making real progress. Employment continues to grow and we see that wages are starting to increase. With moderate growth returning, we must now use the opportunity to combat more forcefully the risk of poverty, inequality of income and of opportunities."