The Markit eurozone Purchasing Managers' Output Index was little changed from October, up to 45.8 from 45.7. A reading below 50 indicates contraction.
A sharper rate of decline in the services sector was offset by an easing of the contraction among manufacturers.
The survey also warned of a 0.5% drop in GDP in the fourth quarter.
Official figures released earlier this month showed that the eurozone economy contracted by 0.1% in the third quarter, between July and September.
"The PMI suggests that the downturn is set to gather pace significantly in the fourth quarter. The final three months of the year could see GDP fall by as much as 0.5%," Chris Williamson, chief economist at Markit said.
"The eurozone economy continued to deteriorate at an alarming pace in November, and is entrenched in the steepest downturn since mid-2009," he added.
Sentiment among services businesses fell to the lowest since March 2009, said Markit.
This article is for general information purposes only. It is not investment advice or a solution to buy or sell securities. Opinions are the authors; not necessarily that of OANDA Corporation or any of its affiliates, subsidiaries, officers or directors. Leveraged trading is high risk and not suitable for all. You could lose all of your deposited funds.