Destro had not featured for Roma in the last six months after suffering a serious knee injury but came on as a second-half substitute against Fiorentina and scored the winner.
"I had been away too long," Destro said to Corriere dello Sport. "I couldn't stand it any more.
"I'm happy that the injury is behind me and to have played was a fantastic feeling.
"We played a great game against a very good side.
"I'm very pleased to have scored but the important thing is that we won.
"We will continue to battle until the end of the season."
The win allowed Roma, who are second in the standings, to end a run of four straight draws and moved the Giallorossi three points behind Serie A leaders Juventus.
The outcome also allowed Roma to break a club record of going 15 straight games without defeat.
"This is an exceptional run," Roma coach Rudi Garcia said. "We are still unbeaten and we are three points behind Juve.
"We are very much in the race for the scudetto."
Roma travel to the San Siro to face AC Milan on December 16 with captain Francesco Totti expected to make a comeback.
Totti has been out of action since October with a hamstring injury.
"I felt it was better not to risk Totti for the game against Fiorentina," Garcia said. "Now he will have a whole week to train in order to prepare in the best possible way for the game against AC Milan."