The Nerazzurri found themselves trailing 3-0 from last week's drubbing at White Hart Lane, but managed to take the tie to extra time thanks to strikes from Antonio Cassano, Rodrigo Palacio and an own goal by William Gallas.
Moratti said that he would have been more disappointed with the outcome had it been in the Champions League.
"The players did what the media did not want to predict, which was bring out all their pride," Moratti told Inter Channel. "We are all very proud of this team and I can only compliment them on their efforts.
"We still went out, but if it had been the Champions League then I would've been much more disappointed with that.
"Tonight we realised that we can count on certain young players and others that are not so young, those who have character and pride. This mix is what must be maintained."
The draw for the quarter-finals takes place in Nyon, Switzerland later today.