Lampard, who was reportedly ready to leave Stamford Bridge, was linked with Inter ever since Jose Mourinho took charge of the Serie A champions.
However, the England midfielder settled for a Blues stay as Inter turned to Ghana playmaker Sulley Ali Muntari.
"He wanted to leave Chelsea, I am certain of that, although it created a lot of anxiety for him and in fact he remained because of family matters," Moratti told Sky Sport Italia.
"He stayed for his father, who he is extremely close to, and for his whole environment. Therefore he was unable to create that split that they expected and we were hoping for.
"Mourinho did hope for this move, but we knew it was going to be difficult.
"So instead we thought of a player who in terms of age and wages is a good deal: I am happy that Sulley Ali Muntari has arrived."
The Inter patron denied that Lampard's snub has resulted in an upset, as he seems to understand the 30-year-old midfielder's decision.
"Was I disappointed by his attitude? Not at all, I found him to be very serious and focused," added Moratti.
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تقرير: دي جريجوريو خارج قائمة يوفنتوس تمهيدا لوصول فيكاريو
"فقدنا الثقة فيه".. اسكتلندا تعلن سحب دعمها لـ إنفانتينو
بعد وصوله إلى برشلونة.. كانسيلو: أنا في المكان الذي أريد أن أكون فيه
تقرير: روما يثق في إتمام صفقة مورا من بورتو.. و50% نسبة إعادة البيع
سيرجيو بوسكيتس يبدأ مسيرته التدريبية مع رديف برشلونة
تقرير: إنتر يجهز عرضا جديدا لضم جونز من ليفربول
أنقذوه من الغرق.. كالياري الإيطالي يعلن نقل لاعبه إلى العناية المركزة
ذا أثلتيك: إبسويتش يضم إنسيسو وواتارا من ستراسبورج












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