Preliminary data showed the weakest reading for service sector activity in 40 months, and expectations for the year ahead were at their lowest since March 2009. Sentiment in Germany, Europe's biggest economy, fell particularly sharply.
Markit's composite purchasing managers' index (PMI) for November stood little changed at 45.8, compared with 45.7 in October.
A fall in the services PMI to 45.7 from 46 was partly offset by a slower rate of decline in manufacturing. Any reading below 50 signals contraction. Markit said the surveys pointed to contraction of 0.5% in the eurozone economy in the fourth quarter.
