It was their first win over Roma in 62 years and Cosmi said: "We achieved something particularly difficult, but not impossible, seeing as football has taught us anything can happen.
The 1-0 victory at the Olimpico was particularly impressive considering goalkeeper Alfonso De Lucia was sent off with 25 minutes left on the clock.
"We were able to get the points despite the circumstances making it very tricky for us. Aside from [Francesco] Tavano's goal, don't forget we lost [Romano] Perticone to injury and had De Lucia dismissed.
"We had a bit of luck, something that my predecessor Gennaro Ruotolo did not."