The Sardinians scored twice in the final 10 minutes to beat the Little Zebras 4-3 at the Stadio Sant'Elia, registering their third win in the last six games in the process.
Speaking after the game, Festa also suggested that he would like stay on as Cagliari boss next season as they seek promotion back to the top flight.
He told Sky Sport Italia: "I am happy about the points that we have picked up in the last seven games. The lads did not give up, they believed in finishing the season off as best they could, and they managed to achieve it.
"I am sorry about relegation but the boys have shown that this squad has good values.
"It would be a great joy to stay at Cagliari. If I do not end up staying, then I will thank the president for the possibility that he has given to me. In other words, coaching my hometown team was an honour. Cagliari has all the credentials to come straight back up to Serie A."
Cagliari finished three points behind 17th-placed Atalanta.