Chelsea won for a record 30th time this season on Sunday, beating relegated Sunderland 5-1 before picking up the the Premier League trophy.
And Conte now wants to complete the double in his first season as Chelsea head coach.
"This is the real danger for us, to think that this season is finished," Conte said.
"To win the title this season becomes great
This season can become fantastic if we are able to win the FA Cup
We must find the right motivation.
"It's important for us to celebrate, but then to find the right fire in our soul to be ready to work very hard this week to prepare and to feel in the right way this game.
"This is a great opportunity to win and to do the double."
Arsenal missed out on the top four for the first time in manager Arsene Wenger's near 21-year tenure, finishing fifth and failing to qualify for Europe's elite club competition.
Conte added: "If you ask me who is the favourite now, I can tell (you) it's Arsenal.
"Arsenal now has only this possibility to find a good season after a win in the FA Cup
For this reason we must pay great attention.
"We must find in ourselves the right motivation, the right anger
The game will be very difficult.
"After I don't know how many years Arsenal missed the Champions League
We must have our antenna very high and prepare in the right way.
"I'm not talking about tactical game, I'm talking about motivation, right fire in ourselves, in our soul, in our heart.
"If we have this in the same proportion as Arsenal, or more, we have the possibility to do the double
Otherwise we risk a lot."
Source : PA
Source: PA