Terry, who was making his first appearance in two months, was dismissed in the 67th minute at Stamford Bridge on Sunday.
Terry, who was making his first appearance in two months, was dismissed in the 67th minute at Stamford Bridge on Sunday after a clumsy last-man challenge on Peterborough striker Lee Angol.
But Conte believes the 36-year-old centre-back, who is out of contract at the end of the season, was hard done by and questioned the decision of referee Kevin Friend.
"I think it wasn't right, this decision from the referee," said the Chelsea manager.
"He didn't take the opponent and also the second reason was because behind John there was Branislav Ivanovic to cover John.
"It's a pity when this happens, because the red card is not good. You have to respect the referee's decision, but in this case maybe we will do an appeal for this situation.
"The situation is very clear and I think John didn't deserve this."
Terry was sidelined with injury at the start of November and has been a spectator during Chelsea's surge to the top of the Premier League table on the back of a 13-game winning run.
The former England defender's future remains uncertain beyond the end of the season, but Conte said it was too early to discuss the possibility of a new deal.
"I think that now we are in January," he said. "First of all this type of decision, it's important to make this decision together (with) the club and not alone.
"I'm pleased for John, because he's showing me great commitment when I ask him to play, when he doesn't play, because he's helping me a lot in the changing room.
"He's showing me to be a good player, but above all a good man.
"Now it's important to continue in this way, because we have to play the second half of the season, the FA Cup. We have a lot of commitments."
Chelsea were leading through goals from Pedro Rodriguez, Michy Batshuayi and Willian before Terry's dismissal.
Tom Nichols replied for third-tier Peterborough, but Pedro wrapped up the win with his second goal.
Conte welcomed the return of centre-back Kurt Zouma following an 11-month absence with a knee injury and also explained why he has recalled Nathan Ake from a loan spell at Bournemouth.
"There were many good things, but the most important was the return of Zouma after 11 months. It was fantastic for him," Conte said.
"I recalled Ake because I think he is showing to be ready to stay in the Chelsea squad. Chelsea is his home.
"He is showing that he deserves to stay in a great team like Chelsea. He gives me an important option because we are playing with three central defenders.
"He can play on the left or in the middle, and we must see in training if he can play at wing-back. We wanted to bring him back because he gives me a good solution."
Conte refused to comment on reports he wants to swap Batshuayi for Swansea City striker Fernando Llorente, but said the young Belgium international had impressed him.
"Michy played a good game," Conte said. "During the game he always stayed into the idea, into the philosophy, into our idea of football. He showed me great commitment and great work-rate.
"Also he scored. For a forward it's always important to score for his confidence. He's a young player, he's working a lot, is improving.
"Now it's important for him to continue in this way and to give me the opportunity to have another solution in our squad."
Peterborough manager Grant McCann said: "It was a good learning curve for our boys.
"We could have come here and defended deeper and tried to frustrate them. But I thought we may as well come here and give it a go. I thought we did that."