Speculation has been rife all season that Conte will be axed as head coach this summer.
The Italian won the Premier League 12 months ago in his first campaign, only for the Blues to finish fifth this term, missing out on Champions League qualification.
A second trophy came at Wembley in what could be Conte's final match as boss, as Eden Hazard's penalty earned a 1-0 win over Jose Mourinho's Manchester United.
"After two years the club knows me very well," Conte said.
"If they want to continue to work with me, they know me. I can't change. My way is always the same: hard work and to build a strong mentality with my players.
"I can't change. I'm this. I'm this and I think my past speaks very clear as a player and as a manager. You can say what you want, but I'm a serial winner.
"I showed this in England in a difficult moment for the club, after 10th place (in 2015-16). I've showed this also today, because we found the right way to win this trophy.
"I'm very happy for the players, I'm very happy for our fans. At the same time I'm happy for the club.
"The decision to charge me (with the job), in two seasons I brought two trophies for this club."
Conte last summer signed an improved contract, but not an extension to the three-year deal agreed on his arrival which expires in June 2019.
The 48-year-old added: "I always say I'm committed to this club, to respect my contract.
"As you know very well our job is not simple. I understand that the club can make a decision, a positive decision, a negative decision. I'm the first to understand.
"I'm the coach of a great, important club, in England and the world. It's right that the club demands of me a lot.
"There is also this possibility (that) with this group of players we did the maximum.
"I have great respect for my club. For sure we'll make the best decision. I'm the first to accept every decision for the future.
"After these two seasons I will always love this colour, these fans, this club. Also if my future must be in a different way."
The Blues can be backed at 13/2 to retain the FA Cup next season, 11/1 to win the Premier League title.
