Catania defended doggedly at Juventus Stadium but the Old Lady made the breakthrough in stoppage time thanks a winner from substitute Emanuele Giaccherini.
Conte believes that his side showed heart to keep fighting and claim the vital three points in their third match in nine days.
He told Sky Italia: "It was a game that we wanted to win at all costs, with great strength and big heart.
"Catania were well organised and it was not easy. This week has been very demanding in terms of physical and mental health, I will give my players a day off tomorrow."