The Sun newspaper reported that Terry, as well as Nathan Ake, Asmir Begovic, Nathaniel Chaolabah and Kurt Zouma were angry with the Italian coach, but the club captain appears to have refuted the claims on Instagram.
Terry has made just 10 appearances this season, most of which came in cup competitions, before he was left out against United, and he is thought to be disappointed at missing the clash against Jose Mourinho's side.
Nevertheless, the former England international is said to have handled the situation professionally and understood Conte's decision on the matter.
The Blues captain has been at the club for more than 20 years, and although his contract is due to expire in the summer, he has previously spoken positively regarding his position in the team.
"Sometimes there’s nothing you can do as a player," he told Steven Gerrard in an interview on BT Sport in January. "I started the first four games of the season and get injured and we lose at home to Liverpool and Arsenal away and the manager is asking “how long till you are back?”
"And then we go 13 games unbeaten and you’re back fit but you can’t get in. And as a player it’s difficult to accept but you have to accept it. I genuinely mean when I say it, but for me I am honestly hoping I don’t play this season which means they keep winning."
Terry expected to have a lesser role at the club, after signing a new deal last summer, and David Luiz has since gone onto take his place after he re-signed from Paris Saint-Germain for £32 million on 31 August 2016.