There is concern over civilian casualties in Afghanistan
"Europe's status has collapsed along with the twin towers in New York," wrote one Italian newspaper last week.
"The European Union ceased to exist", complained a Belgian paper, after the EU summit in Ghent 10 days ago showed that only Europe's militarily powerful states, Britain, France and Germany, had a real say in decisions about the military action in Afghanistan.
Many were shocked to discover that despite European efforts to win a bigger voice in world affairs, the EU and even Nato could be so sidelined in a real international crisis, when the US resolved to take the lead and act.
Public opinion polls show that Americans do appreciate the Europeans' solidarity.
European governments have invoked the collective defence clause of Nato's founding treaty for the first time.
British and German envoys have gone to the Muslim world to shore up the coalition, including countries like Iran, with which the US itself has strained relations.
They have tried to keep alive hopes of peace between Israelis and Palestinians, to make up for a lack of high-profile American efforts.
And the European Union is stepping up aid to Afghanistan, and trying to bring about a stable and representative government there once peace is restored.
Public scepticism
Yet public opinion in parts of Europe - and not only Muslim opinion - is troubled by the war, and by evidence of a rising toll of civilian casualties in the US-led bombing campaign.
In Italy one opinion survey asked people about Osama Bin Laden's words justifying the attacks on the US by affirming that Americans had themselves committed crimes against Arab peoples.
Only 27% of Italians rejected that argument completely, whereas nearly half said there was at least some force to it.
Earlier this year, French Prime Minister Lionel Jospin had accused the US of abdicating world leadership, by standing aloof from international accords on climate change, on the use of landmines and on a new international criminal court.
Now such complaints are less evident, but European Union leaders' distinct views will be apparent at next month's launch of a new world trade round, as well as in US-European rivalry in industry, and environmental questions.
The US is still clearly the more powerful partner in the relationship, but Europe by history and geography may well hold the key to the Americans ability, in the end, to achieve most of their goals.