Roma fought back from a goal down to win 2-1.
Mancini said: "After the defeat against Atalanta we were aware that we had played the best game of the season, unfortunately this is football.
"We were aware of what it meant playing against Inter, we knew we were stronger and we proved it on the pitch by remaining compact and united.
"We suffered, but by playing games like this you bring home the result."
On starting without strikers, he added: "We worked this week not totally together, because of the national teams. The coach had disguised it a bit from us too. We have a very strong attacking pool, those who started did very well, (Tammy) Abraham pressed a lot when he entered. If you want to achieve goals you have to have a strong squad."