Morgan Gibbs-White struck early for Forest as the hosts won the second-leg 1-0 and their Europa League quarterfinal 2-1 on aggregate.
Farioli said afterwards: "Just as in the first leg, we had a massive chance in the first three minutes.
"We didn't convert, and after the red card, it was more about getting into half-time to have the opportunity to change a few things; a few players, but especially to have a proper adjustment tactically."
The Italian also said: "I think the reaction of the team has been fantastic. In the second half, we changed gear. If you make a calculation of the two matches, it's quite clear who deserved to win, but sometimes ‘deserve’ is not enough.
"You need to put the ball in the net, and we didn't do it, especially in the Dragão."