But Zaccheroni warned they are not qualified for the next round yet, despite their win in Holland - thanks to a brace from Amauri.
He said: "I had expected us to struggle and told my players the same. Ajax may be missing something in terms of star names, but they play very well as a collective.
"We earned a result that does not qualify us yet, but it is very important for our chances."
On Amauri, Zaccheroni added: "I repeat what I said when he hadn't scored for four months - you never play with 10 men if Amauri is in the side.
"He knows how to play with his back to goal and even better when facing the net. We put him in a position to score and he did what he does best."