Dante says Nice's 1-0 Coupe de France final defeat to Nantes on Saturday will "hurt for a long time".
Ludovic Blas scored the only goal of the game from the penalty spot in the first minute of the second half at the Stade de France.
Blas emphatically drilled home his spot-kick after Hicham Boudaoui handled and that was enough for Nantes to win their first major trophy for 21 years.
Nice were left to rue their lack of a cutting edge as they failed to end a trophy drought that stretches back to 1997, when they lifted the Coupe de France for a third time.
Captain Dante was left to reflect on a painful missed opportunity and warned Christophe Galtier's side must respond when they face St Etienne in Ligue 1 on Wednesday, with European qualification not secured.
The Brazilian defender said: "A lot of sadness. We are very disappointed because we really wanted to give this to our supporters and the people that have been waiting for this for so long, but we didn't manage to do so.
"It will hurt for a long time but we need to quickly lift our heads. We have a very important match on Wednesday."
Nice boss Galtier felt his side did not do themselves justice in Paris.
He said: "My feeling is disappointment. When you reach the final and you play for this magnificent trophy, you do everything possible to try to win it.
"The big regret I have is about our technical quality on an offensive level. We had very little success in what we undertook. We showed too much haste in the game."
He added: "It is a great regret, a very great disappointment."