Flash data showed that manufacturing and services output fell below expectations in September, according to figures from Markit.
The composite purchasing manager's index (PMI) came in at 53.9, down from 54.3 in August and below expectations for a reading of 54.1 from analysts polled by Reuters.
In terms of quarterly growth, however, Markit said the survey data pointed to "steady growth of the euro zone economy at the end of the third quarter."
"Moreover, faster growth of new work and backlogs of orders point to continued expansion in coming months. Selling prices were meanwhile stable despite sharply reduced commodity prices," it said.
Chris Williamson, Markit's chief economist, commented on the data, saying there were still concerns over a lack of job creation. "The September PMI surveys indicate a further steady expansion of the euro zone economy, but there remains a worrying failure of growth to accelerate to a pace sufficient to generate either higher inflation or strong job creation."
Breaking down the figures in terms of the euro zone's two largest economies, Germany and France, the picture was also gloomy.
While the rate of expansion in business activity in France picked up from the near-stagnation seen in August it remained only modest, with France's composite PMI reaching 51.4 in September, up from 50.2 in August. In Germany, the same measure saw the index at 54.3, down from 55.0 the previous month.
The data pointed to 0.4 percent growth of the German economy in the third quarter, but a mere 0.1 percent expansion in France, according to Markit's Williamson, who said that "France remains a particular concern."