France accompanied the Azzurri to the European championship after the latter's decisive away win, thanks to a 90th minute killer goal from veteran defender Christian Panucci.
The score line congealed the Scots at 24 points in third place, one point adrift of France, who still have a game in hand.
However, Gattuso conceded that helping Les Bleus was the only negative aspect of his side's achievement.
"I am proud of reaching qualification with this national team. But it annoys because I know we have also helped France qualify," the Milan man told reporters.
Draw Specialists
The tenacious midfielder aimed a swipe at France coach Raymond Domenech, who claimed earlier that Italy won because his words 'motivated them'.
Domenech claimed that describing Italy as 'draw specialists' inflamed the Italians' desire to win the game.
"Domenech always has to say something, he doesn't deserve to go through really. Now I hope we will play them again in the Euros and give them a lesson," said Gattuso.
The edgy state between the two European powerhouses was initiated at the 2006 World Cup final, which saw Italy grab a 5-4 penalty shootout victory in Germany.
نرشح لكم
كين: التتويج بالكرة الذهبية سيكون نجاحا هائلا لي
كادينا سير: الاتحاد الأوروبي يؤكد استلام مستندات ريال مدريد بشأن قضية نيجريرا
جيرارد مارتن: حمزة عبد الكريم لاعب رائع.. وهذا ما يميزه
بعد وقوفه أمام المحكمة.. إيفان توني يطالب ببراءته من تهم الاعتداء
كوني: إيطاليا في حقبة معقدة.. وزيدان منحنا الحرية
تدخل حكومي برتغالي لحل أزمة كريستيانو رونالدو










مباشر كأس العالم للأندية - الأهلي ضد الزمالك.. انطلاق المباراة بعد قليل
الغندور بدلا من عاشور.. في الجول يكشف القائمة الدولية للحكام