Sergio Pellissier and Elvis Abbruscato struck the goals for Chievo.
"We are not mathematically safe yet and I think it will only take another one or two points to achieve that," countered Di Carlo.
"Today's victory was a very important result. Livorno put us under pressure in the second half, but fortunately we got the second goal, which felt like a huge weight off our shoulders.
"The credit goes to the team, who knew when to cling on and wait for the right moment."