The Nerazzurri led 2-0 in that encounter thanks to goals from Ciccio Caputo and Romelu Lukaku, but were pegged back to 2-2.
Another strike from Borja Valero after 85 minutes seemed to have won the match for Conte’s side but Giangiacomo Magnani’s late equaliser cost them two points and dealt them a major blow in the title race. It was shortly after that effort that Conte saw yellow.
“I think we deserved much more considering how much we created, whereas I don’t recall any Samir Handanovic saves,” Conte said of the match in his press conference. “It’s something we keep repeating in this pattern and are paying a heavy price.
"I am very disappointed and so are the lads. When you play this type of game and put so much into it, you have the chance to win despite the difficulties in the key area of midfield, you have to take home the three points. We didn’t do that, it’s disappointing and troubling.
“We had the chances to finish it and we didn’t. I don’t know what more we can do other than keep working.
“I am happy with the performance, we’ve got to be more careful on the details. That is where we can grow and improve.”
To make matters worse for Inter, who are eight points behind leaders Juventus with 11 fixtures remaining and four back from second-placed Lazio, they will have to do without centre-back Milan Skriniar after he was dismissed, rendering him unavailable for the next three games.
The Slovakia international, who was dismissed for “making an offensive remark to the referee along with a blasphemous exclamation” has also been fined €10,000 (£9,000/$11,200).
As well as the trip to Parma at the weekend, he will sit out a home encounter with Brescia next Wednesday as well as a clash with Bologna in Milan on July 5.