The Blues went to the Italian capital knowing a win would have booked their place in the last-16 of the tournament with two matches remaining.
However, they got off to a nightmare start when Stephan El Shaarawy scored after 38 seconds to put Roma ahead.
This season we have to dig very deep if we want to be competitive and fight for something important. If we are not ready to dig deeper, we can have this type of game.
He then and pounced on an Antonio Rudiger error to make it 2-0 after 36 minutes, before Diego Perotti struck a fine third after 63 minutes.
The defeat saw Chelsea drop to second, a point behind their opponents in Group C and, while they look set to qualify for the knockout stages after third-placed Atletico Madrid were held to a 1-1 home draw against ten-man Qarabag, Conte has said they will not win anything this season unless they make huge improvements.
He said: “This season we have to dig very deep if we want to be competitive and fight for something important. If we are not ready to dig deeper, we can have this type of game.
“This season will be very difficult if we don’t understand quickly the right way that we have to go. Last season we showed great hunger, great will to do something of importance. Last season we won the league and did a miracle.
“If we think that only because our name is Chelsea and the opponent has fear for the name Chelsea, I think this is not the right way.
“We must find the hunger that we showed in all last season and in this season sometimes. We have to try to find the strength to understand and to use this loss in the right way.”