The world champions beat a 10-man France side, who was hit by an early blow as star man Franck Ribery left the pitch on a stretcher.
Donadoni did admit that there was some fortune, but has no doubts that his team deserved a victory in Zurich.
"The victory is a reward for the whole group and especially the players who have worked so hard over the last two years," said the Italy tactician.
"The players deserve the credit. We did get some breaks. Franck Ribery's injury made it hard for the French and there was also the deflection in the second goal. But I wouldn't say we were lucky because we created a lot of chances."
Formidable
The former AC Milan winger showed a sign of respect to his opponents, who handed the Italians their only defeat in the qualifying campaign.
"It's a great win because we were up against a formidable opponent. I want to congratulate France, who never stopped running and put us in difficulty despite playing with ten men," Don added.