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.