Both still remain clearly above the 50.0 mark that divides growth from contraction. The survey was conducted Dec. 4-14, straddling the time when global central banks said they would join forces to aid a credit crisis gripping markets.
"A significant part of the decline is probably related to the financial sector," said Jacques Cailloux, chief euro area economist at RBS.
However, he stressed a fall in the services PMI was not likely the result of contagion from the credit crunch spreading, but rather part of a wider slowdown in the economy.
The larger fall in the services sector hit the composite index, which sank to 53.3 from 54.1, its lowest level since August 2005.
The services PMI was largely dragged down by a two-point drop in incoming new business to 52.0 in December, tumbling to a level not seen since March 2005.
Yet the business expectations index for the services sector picked up in December to 60.7 from 58.5, giving a signal of a possible pick-up in activity to come.
Inflation clouds lingered, with the prices charged index climbing to 54.0 from 53.6 the previous month, back to levels seen in better times for the euro zone economy in June.
The input prices index eased slightly to 63.2 from 63.4 in November, still close to a seven-year high as energy and food prices soared. There was some evidence of a pick-up in wages.
Employment held at a robust 54.5 in December, just shy of the 54.6 hit in November, but still way down on the 56.4 touched in July.
On the manufacturing side, new orders growth slipped to 51.7 from 52.8, while new export orders eased to 52.3 from 52.5. But the decline overall was much less pronounced than in the services sector.
"The data does not suggest we are going to lose much more momentum in the coming months. There is a sense of stabilization at a weaker level," said Cailloux.
Indeed, employment in the sector remained robust, holding at the 52.1 hit in November, but down from summer highs.
Higher oil and energy prices also saw price pressures stay stubbornly high. The factory input prices index eased slightly to 61.3 from 61.7, but clients bore the brunt of some of the increase as the output prices index rose to 53.9 from 53.6.