Conte's side cruised to a 2-0 win over Southampton in Sunday's semi-final to set up a heavyweight clash with United at Wembley on May 19.
But Conte doesn't believe Chelsea, beaten by Arsenal 2-1 in last year's final despite going into the match as Premier League champions, will be regarded as favourites to lift the famous old trophy.
"This final is a game between two great teams. In my mind I can tell you we played the final as favourites against Arsenal," he told reporters after his team's triumph.
"I think in this season we arrive not as favourites. But then last season we lost the final even though we were expected to win."
Given their long-running feud, there will be as much attention on the two managers on Cup final day as there will be on the players.
Conte addressed the rivalry: "I think with Jose, we have clarified the situation. This is the most important thing. There is not a problem between him and I.
"We are talking about two managers with strong characters, two winners. In your heart and your blood there is the will to win.
He continued: "For sure, we want to try to win the trophy, in the same way United do. I have great respect for United and Mourinho's story."