The big-spending Spanish giants had countless efforts on goal but a mixture of good goalkeeping from Ajax goalie Maarten Stekelenburg, the woodwork and poor finishing saved Martin Jol's Ajax from a heavy defeat in their Group G opener.
It turned out easier for the English giants of Arsenal and Chelsea to find net before their less illustrious opponents.
Cesc Fabregas and Carlos Vela each scored twice in Arsenal's 6-0 rout of Portuguese side Braga, while Nicolas Anelka's double helped Chelsea surge to a 4-1 victory over newcomer Zilina.