Merih Demiral scored twice in a 2-1 Turkey win in Leipzig, with the victory sending the team into the quarter-finals of the European Championship.
Montella lavished praise on his side for the success, which has set up a last-eight contest with Netherlands.
"I'm very proud of the spirit we showed on the pitch," Montella told reporters during his post-match press conference. "It's outstanding for a coach when you're able to see that.
"Besides our formation, our gameplan and our tactics I saw Turkish heart today, and that's what I love about this country."
Demiral netted a brace in Turkey win
Turkey suffered a 6-1 defeat to Austria when the two teams locked horns in a friendly back in March, and Montella called that contest "a horrible stain" on his career.
"A horrible stain on my career. That's what I was waiting for, to try and get this m off my back. We as coaches are just like footballers, we're competitors," the head coach added.
"I had this competitive instinct because we wanted to change that result, it was a friendly but there's no such thing as a friendly."
Montella was also asked to compare his success with Turkey with his Suppercoppa Italiana victory in 2016 while in charge of AC Milan.
Turkey will face Netherlands in the quarter-finals
"One victory does not cancel another one," the Italian added. "If I look at the past, lifting a cup with Milan was marvellous because not many coaches have done it in their careers.
"This is on a different level, a different dimension. It's at a European level and it represents a country, not a club. I can't compare them, but perhaps this one [means] a little bit more because it's happening now, and I am enjoying it."
Montella also praised his goalkeeper Mert Gunok, who produced an incredible save late on to keep out an effort from Christoph Baumgartner.
"I'm happy for him, happy for the team and the country, happy for the group and what we've created here. Well done to Mert, it's his job to make saves and we're very happy that he'd made a match-winning save in the final minute," he added.
Turkey will tackle Netherlands in the quarter-finals of Euro 2024 on Saturday, and a victory in that match would see them battle either England or Switzerland in the semi-finals.