Conte is unhappy that Southgate revealed Danny Drinkwater rejected a late call to be involved in England's recent games against Germany and Brazil.
The 27-year-old told Southgate he wasn't fit due to sustaining another knock to his injured calf, which has restricted him to just one start for Chelsea since joining from Leicester in the summer.
Standard Sport revealed last week that Drinkwater is still desperate to play for England and hasn't given up hope of making the World Cup squad next summer.
But that hasn't stopped Drinkwater receiving a lot of criticism and Conte, who was in charge of Italy between 2014-16, has urged Southgate to get in touch with him if he has any questions about a player's injury.
Conte, who also has England defender Gary Cahill in his Chelsea squad, said: "It's a pity that a player had to pay for this misunderstanding.
"Sometimes there is a way, which is very easy, to try to call the coach before and to ask 'is it ok, I can do this? Is this player good or does he have a problem? Is he tired or not?'
"I am telling you this because I was coach for the national team. In this way you can avoid a misunderstanding because about Drinkwater it was a misunderstanding. He was injured and also he wasn't really 100 per cent fit to go with the national team.
"If someone asks me I can explain and if the coach wants to take the same decision it is ok, but it is important to have more relationship between the coach and the coach of the national team.
"It was the same for us with Eden Hazard (in late August when he was returning to fitness from a fractured ankle). Then I spoke with (Belgium coach) Roberto Martinez, I said yes and then he played.
"I am ready to help every single national team coach because I had this fantastic experience and I understand very well the problems. I am more open than before when I was the coach of Juventus but sometimes there isn't the communication.
"Drinkwater was very honest and he doesn't deserve to be attacked from the press or the people because he was very honest.
"In this situation every single player wants to go with the national and we have to appreciate his behaviour and commitment."
However, Conte insists that there has been no major fall-out with Southgate over the saga and hopes they can have a beneficial rapport going forward.
He added: "There is a good relationship (between him and Southgate). Last season he came to Cobham when he was the Under-21 coach.
"He has an assistant that has a great friendship with me in (former Chelsea assistant Steve Holland) because he is a really good person, an intelligent person.
"If they want I am ready to help every national team coach, not only the coach of the English."