"It was the game we expected – tough and against a side that didn't do us any favors. We also had quite a few players missing," Donadoni said as reported by Calcio Italia magazine.
"The lads always believed in this result and I have to praise everyone, from those who played 90 minutes to the ones in the stands."
The World Cup champions have been struggling so far under the new management, having endured one draw and two defeats.
Still, the Italian coach was able to see where the team had improved in their much needed victory.
"I was impressed by the fact we didn't let ourselves panic in attempts to score early on, as that can lead to confusion. It's a sign of great maturity in the squad," said the former Livorno manager.
Second-half goals from defender Massimo Oddo and striker Luca Toni gave the Azzurri their first victory in their Group B of the Euro 2008 qualifiers.
"The three strikers were all good, especially considering Vincenzo Iaquinta was playing in a role he is unaccustomed to.”
For Donadoni, it was the high pressure performance of the team that allowed them to contain the Ukraine's efforts.
"We fought for every ball and knew how to soak up pressure, even though Ukraine were only really dangerous from distance and with set-pieces. That's because we closed them down and never allowed them to get near the goal," Donadoni said.
Still, despite Italy's improved performance the crowd started the match skeptical of the team's efforts, there were jeers before the kick-off and some fans booed Donadoni's name.
"I didn't hear those, all I heard were supporters cheering on Italy," the former AC Milan midfielder said.
"Perhaps nobody believed so many people would turn up to the match. We hope to earn our place in the fans' hearts with some good performances."
While the national team's next test is away to Georgia on Wednesday evening, Donadoni is sure that the Azzurri still stand a chance at qualifying.
"I saw a great team spirit today and the squad has character. Our path to Euro 2008 is a difficult one, but France lost in Scotland today, proving it's a tough Group.
"We have to pick up points wherever we can."
Italy are currently in third place in Group B with four points, tied with Lithuania. At 100 percent Scotland is leading with nine points, followed by France on six points.