The Juventus boss was furious with criticism from the iconic Italian trainer, but the current Russia coach has looked to mend his public relationship with his compatriot
The former Bianconeri boss criticised the current trainer of the Turin club last week, to which Conte responded by saying the Russia coach lacked respect for sticking his nose in and insinuating Serie A is an amateur league now.
Capello has sought to smooth relations by applauding Conte's work with the reigning Italian champions, but defended his comments on the coach's decision to cancel a day off after Juve conceded a late goal against Hellas Verona earlier in February.
"Conte is doing a good job and demonstrating his value," the ex-England boss told Italian outlets.
"Everyone controls teams the way you think best. I never said I was against the decisions he took, I just questioned the reason that led him to cancel the day off and that I was against this kind of method.
"I do not punish people if they did not do something wrong. I never did it."
Juventus - who beat Chievo 3-1 on Sunday - are back in action on Thursday at home to Turkish side Trabzonspor in the first leg of their last-32 Europa League tie.