"The latest hard data, particularly yesterday's industrial production numbers, have taken away some of the optimism created by strong sentiment indicators," Carsten Brzeski, senior economist at ING, told CNBC.
"The good news is that the recovery continues – the bad news is that the recovery remains weak."
Brzeski expected GDP growth for the fourth quarter to come in around 0.2 percent, as did Societe Generale.
(Read more: Why euro zone slowdown should worry the world)
"The December industrial production figures suggest that the economic momentum is unlikely to improve going into (the first quarter of 2014)," Soc Gen economists led by Michala Marcussen said in a research note.
"Overall, we are still heading towards a 'weak and uneven' recovery, as highlighted by European Central Bank (ECB) President Mario Draghi."
'Race to the bottom'
One of the themes of the euro zone's recovery - since it exited its longest recession in over 40 years in the second quarter of 2013 - has been a divergence between the performance of the region's economies.
Germany – sometimes dubbed the "powerhouse of Europe" – has generally outperformed its neighbors, while the economies of France and Spain and some others in "peripheral" Europe have often disappointed.
There are signs this gap could be narrowing, however.
Taking the industrial production data on a country level, for instance, almost all euro zone countries posted a fall in output. France's slipped by 0.3 percent while Spain's fell by 0.2 percent – but Germany's dropped 0.7 percent.
"Looking at the growth perspective , there is still a divergence in the euro zone, but this gap between the countries is reducing," Barclays' Menut said. "German will remain the growth driver, but we expect France, for instance, to continue on a moderate growth trend."