Drinkwater declined the opportunity to join up with the Three Lions, explaining that he felt pain in his calf after Chelsea's 1-0 win over Manchester United, where he came off the bench in the second half.
The Chelsea midfielder also wanted to stay a Cobham training centre to build up his fitness ahead of a busy festive schedule and Conte believes any criticisms aimed at the midfielder are unwarranted.
Expressing his frustration at not being consulted over the call-up, Conte said: "Sometimes there is a very easy way [to solve this problem], because before you think to call someone [a player to the national team], try to call the [club] coach and ask: 'Is it okay? Can I do this?' I am telling you this because I was coach for the [Italy] national team.
"In this way you can avoid a misunderstanding because I think, with Drinkwater, it was a misunderstanding. He was injured and also I think he wasn't really 100 per cent fit to go with the national team.
"If someone asks me this then I can explain and if the coach wants to take the same decision, it is okay, but it is important to have more of a relationship between the [club's] coach and the coach of the national team.
"It was the same for me. I spoke with Roberto Martinez [when Eden Hazard was coming back from injury] and explained 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 of the national teams.
"For sure, I am more open than before when I was the coach of Juventus but sometimes there isn't the communication. Before you call the player, if you call the coach and ask ‘is this player good or does he have a problem? Is he tired or not?’ Only [do] this [first] and then decide to call or not call a player.
"Otherwise the player has to pay for this misunderstanding. Drinkwater was very honest and he doesn't deserve to be attacked from the press or from the public because he was very honest. In this situation every single player wants to go with the national [team]. [He is thinking] 'The national team is calling me' and we have to appreciate his behaviour and commitment.
"There is a good relationship [with Southgate]. Last season he came to Cobham when he was the Under-21 coach. He also has an assistant that has a great friendship with me in 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 England."
Chelsea loan stars Ruben Loftus-Cheek and Tammy Abraham made their debuts for their country during the international break and Conte admits he would be delighted if they made it into England's squad for the World Cup.
"First of all, I was very happy for these calls with the national team," he added. "Don't forget that these are friendly games. I was a coach in the national team and this is the right moment to try to find and give the opportunities to young players.
"Don’t forget, Gareth Southgate was the coach of the Under-21s and he knows these young players very well. I would be very happy for Southgate to call them for the World Cup. It would be a great opportunity for them and it means they are really ready to play for a great team.
"You have to understand there are two different moments. If I call up a young player for World Cup qualifier, this is one thing. If you try to call a young player up during a friendly game and after you are sure you're playing at the World Cup, then I think this is another thing because you can experiment.
"It is a different pressure. We must be intelligent to understand these two different situations. You can [play young players] when the result is not important. For the club, the result is always important otherwise they sack the manager and there is the pressure of the press, it is totally different.
"I wanted this decision [for them] to go [on loan] and play regularly for their development. If the player understands this and the young player wants this, it is very difficult to keep him in the team. Why would you try and go against his will? For Ruben, it was the best solution for him.
"It was the best solution for Andreas Christensen. It is the best for Tammy Abraham. I think it is the best for them and the club, but if they didn't want to go and play on loan, maybe they would be here [in the Chelsea squad]."
Conte has mixed news on the injury front ahead of Saturday's meeting with West Brom, with Hazard, David Luiz and Gary Cahill all available but Victor Moses and Michy Batshuayi both absent.
On the Belgian's injury, Conte said: "He went with the national team and then came back with this problem but [that was] three or four days before Manchester United. He took a knock in his ankle but for the game against Manchester United he was available - he then felt more pain in his ankle.
"Now he is not available for the national team and also us. We have to wait and go day-by-day to understand why he has this type of problem in his ankle. It is better to speak with the doctor about this situation. It was an old injury and now he is feeling again the pain in his ankle.
"I want to explain it to you but I think it is better to speak with the doctor to explain what the problem is."