The Belgian superstar joined Real Madrid this summer after bagging 16 goals and 15 assists last season.
But Barkley feels the Blues have enough quality to cover Hazard's production.
"Everyone in the squad understands he was a great player but he is gone.
"He has new challenges now and we have to replace his goals and create the chances. We have that much quality in the squad we will all step up to the plate.
"Last season when Eden wasn't playing we still won games, we still created chances. We know he is an exceptional player but we have exceptional players in the squad.
"We have young ones that will step up and produce the goods as well. We have Callum [Hudson-Odoi] coming back from injury and we have signed Christian Pulisic - he is an exceptional talent.
"We have wingers who can create from tight positions, players who can shoot from distance and strikers - young and experienced - who are hungry for goals."