Chelsea are now left fighting on two fronts in the remaining weeks of the season, as they attempt to lift the FA Cup for a fifth time in 11 years, while also finishing in the top four of the Premier League.
Conte insists that all he can ask from his players is to continue giving their all, with Sunday's win at Leicester coming hot on the heels of a heavy loss against Barcelona in the Champions League.
"It was a tough game but we knew this. The last game at home we suffered a lot against Leicester," he told BBC Sport. "We must be pleased today. I saw a good performance and great character from my team. After the game in the Champions League when we spent a lot of energy they showed good heart to beat Leicester.
"When you arrive at this point, every game is difficult. Southampton have just changed coach but now it is important to be happy and to go for another game at Wembley. We will try to do our best to reach the final. We want to give satisfaction to our fans.
"I think that for us our target is to try and do our best. To work hard with the players. I must be pleased with the commitment of the players. If you can win a trophy it is important for a team like Chelsea. But the most important thing is for us to fight until the end in every competition. We will try to reach the final."
Chelsea return to action on April 1 with a home league match against Tottenham Hotspur, who sit directly above them in the table.